GELE Geodesy — Geodetic Control NetworksExam Answer Templates
Geodetic Control Networks answer templates for the GELE 2026. These are the step-by-step approaches that work on Professional Regulation Commission (PRC) — Board of Geodetic Engineering's most common question formats in the GELE Geodesy subtest. Memorise the structure, practise with real questions, then execute on exam day.
Exam context
Professional Regulation Commission (PRC) — Board of Geodetic Engineering runs the Geodetic Engineer Licensure Examination on September 2026. Its Geodesy section sits under a "Core" weighting, and Geodetic Control Networks is the 4th chapter in the 6-chapter GELE Geodesy rotation. The GELE passing mark is 70% weighted average, no sub-test below 50%, and the most recent 2026 paper drew about a meaningful share of questions from Geodesy.
Geodetic Control Networks - Exam Answer Templates
Proper answer writing is the bridge between knowing the material and earning full marks on the PRC Geodetic Engineer Licensure Examination. Many examinees lose marks not because they lack knowledge, but because their answers are poorly structured, missing key technical terms, or lack the step-by-step clarity that examiners reward. These templates show you exactly how a perfect answer looks for each mark level — from a one-line definition to a fully worked numerical problem. Study the model answers, memorize the key phrases, and apply the scoring breakdown logic to every question you practice. In Geodesy — particularly in Geodetic Control Networks — examiners reward precision: correct law of sines application, correct tolerance formula usage, proper order hierarchy language, and logical, organized computation. Use these templates as your writing standard on exam day.
Templates
Define triangulation as a method of horizontal control surveying. [1 mark]
Marks
1
Topic
Horizontal Control — Triangulation
Difficulty
easy
Template Id
T1
Examiner Tip
The single mark is for the complete concept: angles measured + baseline + Law of Sines. Any two of the three components without the third will likely receive 0 at strict marking.
Model Answer
Triangulation is a method of horizontal control surveying in which all the interior angles of a network of connected triangles are measured, together with at least one baseline distance, and the unknown side lengths are computed using the Law of Sines.
Question Type
very_short_answer
Answer Structure
- One complete sentence: name the method + what is measured (angles + baseline) + how unknowns are found (Law of Sines) [1 mark]
Scoring Breakdown
Marks
1
Criteria
Correct definition including the concepts of angle measurement, baseline measurement, and Law of Sines computation
Common Mark Deductions
- Writing 'distances are measured' instead of 'angles are measured' — this describes trilateration, not triangulation
- Omitting the baseline — a triangle net without a baseline has no scale
- Vague answer such as 'a method using triangles' with no mention of what is measured
Key Phrases To Include
- angles of a network of triangles
- baseline
- Law of Sines
- horizontal control
Define trilateration and state one condition under which it is preferred over triangulation. [1 mark]
Marks
1
Topic
Horizontal Control — Trilateration
Difficulty
easy
Template Id
T2
Examiner Tip
The examiner wants to see the contrast with triangulation — emphasize 'sides measured' vs. 'angles measured' to earn the mark cleanly.
Model Answer
Trilateration is a method of horizontal control surveying in which all the sides of a network of triangles are measured using electronic distance measurement (EDM), and the angles are computed from the measured distances. It is preferred when EDM equipment is available and angular measurements are difficult or time-consuming.
Question Type
very_short_answer
Answer Structure
- Part 1: Definition — sides measured by EDM, angles computed [½ mark conceptually]
- Part 2: One valid condition for preference [½ mark conceptually — awarded as a whole unit at 1 mark]
Scoring Breakdown
Marks
1
Criteria
Correct definition stating that distances (not angles) are the primary measurements, plus a valid condition of preference
Common Mark Deductions
- Confusing trilateration (sides measured) with triangulation (angles measured)
- Omitting the EDM reference — modern trilateration is EDM-based
- Giving a condition that actually favors triangulation instead
Key Phrases To Include
- sides measured
- EDM (electronic distance measurement)
- angles are computed
- horizontal control
What is meant by 'working from the whole to the part' in the establishment of a geodetic control network? [1 mark]
Marks
1
Topic
Orders of Accuracy — Control Hierarchy
Difficulty
easy
Template Id
T3
Examiner Tip
This is a classic board-exam concept question. The two key ideas are: direction (higher → lower order) and the prohibition (never lower → higher). State both for a complete answer.
Model Answer
Working from the whole to the part means that surveys always begin from higher-order control points (which have greater accuracy and wider spacing) and progressively densify to lower-order control points. Lower-order surveys are never used as the basis for extending higher-order control.
Question Type
very_short_answer
Answer Structure
- State the principle: higher-order → lower-order [1 mark]; the reverse prohibition is a bonus clarifier
Scoring Breakdown
Marks
1
Criteria
Correctly states that control is established from higher-order (greater accuracy) down to lower-order, never the reverse
Common Mark Deductions
- Describing it vaguely as 'starting from a big area' without mentioning order hierarchy
- Reversing the direction — saying lower-order is established first
Key Phrases To Include
- higher-order to lower-order
- densify
- never the reverse
- accuracy hierarchy
In a triangulation survey, triangle ABC has a measured baseline AB = 6 500 m, angle A = 62°, and angle B = 75°. Compute side BC. [2 marks]
Marks
2
Topic
Triangulation — Law of Sines Computation
Difficulty
easy
Template Id
T4
Examiner Tip
The angle-sum check (Step 1) is a separate mark. Write it out even though it looks trivial — skipping it costs a mark. Always label which side is opposite which angle.
Model Answer
Given: AB = 6 500 m, ∠A = 62°, ∠B = 75° Step 1 — Find angle C: ∠C = 180° − 62° − 75° = 43° Step 2 — Apply the Law of Sines (BC is opposite ∠A): BC / sin A = AB / sin C BC = AB × (sin A / sin C) BC = 6 500 × (sin 62° / sin 43°) BC = 6 500 × (0.88295 / 0.68200) BC = 6 500 × 1.29464 BC ≈ 8 415 m
Question Type
numerical
Answer Structure
- Step 1: Compute angle C = 180° − A − B [1 mark]
- Step 2: Correct Law of Sines setup and final numerical answer with units [1 mark]
Scoring Breakdown
Marks
1
Criteria
Correctly finds angle C = 43° by angle-sum check
Marks
1
Criteria
Correctly identifies BC is opposite angle A, applies Law of Sines, and arrives at BC ≈ 8 415 m with units
Common Mark Deductions
- Pairing BC with the wrong opposite angle (e.g., using sin B instead of sin A)
- Omitting the angle-sum step — examiner requires it explicitly
- Giving the answer without units (metres)
Key Phrases To Include
- ∠C = 180° − A − B
- BC / sin A = AB / sin C
- Law of Sines
- opposite angle
A second-order class I leveling loop has a total circuit length of 25 km. Using a tolerance of 8 mm√K (where K is in km), determine the allowable misclosure for this loop. [2 marks]
Marks
2
Topic
Vertical Control — Leveling Misclosure Tolerance
Difficulty
easy
Template Id
T5
Examiner Tip
Memorize T = k√K permanently. Board exams vary the values of k (4, 8, 12 mm) and K, but the formula never changes. Always convert K to km before substituting.
Model Answer
Given: K = 25 km, tolerance constant k = 8 mm/√km Formula: T = k√K Substitution: T = 8 × √25 T = 8 × 5 T = 40 mm The allowable misclosure for this leveling loop is 40 mm.
Question Type
numerical
Answer Structure
- State the formula T = k√K and identify the given values [1 mark]
- Correct substitution and final numerical answer in mm [1 mark]
Scoring Breakdown
Marks
1
Criteria
Writes the correct tolerance formula T = k√K and correctly identifies k = 8 and K = 25
Marks
1
Criteria
Arrives at T = 40 mm with correct units
Common Mark Deductions
- Using T = k × K (linear, not square root) — this is the most frequent error
- Using K in metres instead of kilometres — always check units before substituting
- Omitting units on the final answer
Key Phrases To Include
- T = k√K
- K in km
- tolerance
- misclosure
Differentiate triangulation from trilateration in terms of field measurements taken and the computational procedure used to determine the remaining elements of the control network. [3 marks]
Marks
3
Topic
Horizontal Control Methods — Triangulation vs. Trilateration
Difficulty
medium
Template Id
T6
Examiner Tip
Structure your answer with numbered or bulleted points using the same category (measurements, computation, application) for both methods side-by-side. Parallel structure signals thoroughness.
Model Answer
Triangulation vs. Trilateration: 1. Field Measurements: • Triangulation: All interior angles of the triangle network are measured in the field. At least one baseline distance is also measured to provide scale to the network. • Trilateration: All sides of the triangle network are measured in the field using electronic distance measurement (EDM). No direct angular measurements are made. 2. Computational Procedure: • Triangulation: The unknown side lengths are computed using the Law of Sines: (side / sin opposite angle). Only angles are adjusted during network adjustment. • Trilateration: Angles are computed from the measured distances using the Law of Cosines: cos A = (b² + c² − a²) / (2bc). Only distances are adjusted during network adjustment. 3. Accuracy Consideration: • Triangulation is preferred in mountainous terrain where line-of-sight distances are long but angular measurements are still feasible with a theodolite. • Trilateration is preferred when precise EDM equipment is available and line clearance for distance measurement is practicable.
Question Type
short_answer
Answer Structure
- Point 1: Field measurements for each method (angles + baseline vs. all sides) [1 mark]
- Point 2: Computational method used (Law of Sines vs. Law of Cosines) [1 mark]
- Point 3: Condition of preference / accuracy context [1 mark]
Scoring Breakdown
Marks
1
Criteria
Correctly states that triangulation measures angles (+1 baseline) while trilateration measures all distances
Marks
1
Criteria
Correctly names Law of Sines for triangulation and Law of Cosines for trilateration in the computation
Marks
1
Criteria
Provides a meaningful context or advantage for each method, showing understanding of application
Common Mark Deductions
- Stating 'triangulation uses distances' — this confuses the two methods
- Omitting the Law of Cosines for trilateration computation
- Writing a narrative that mixes the two methods without clear separation
Key Phrases To Include
- angles measured
- baseline
- Law of Sines
- all sides measured
- EDM
- Law of Cosines
- network adjustment
Explain the concept of 'strength of figure' in triangulation networks. What angular range ensures a well-conditioned triangle? [3 marks]
Marks
3
Topic
Triangulation — Strength of Figure
Difficulty
medium
Template Id
T7
Examiner Tip
Always connect the criterion (angle range) back to the mathematical reason (sine behavior). Examiners reward the cause-and-effect chain, not just a memorized number.
Model Answer
Strength of Figure in Triangulation: Definition: Strength of figure is a measure of how sensitively the computed side lengths in a triangulation network respond to errors in the measured angles. A network with high strength of figure produces large, reliable side values with minimal error amplification. Basis: When a side is computed by the Law of Sines (side = baseline × sin A / sin C), the accuracy of the result depends on the rate of change of the sine function at the angles used. Near 0° or 180°, sine changes rapidly for small angle changes, so a small angular measurement error causes a large error in the computed side. Near 90°, sine changes slowly, making the computation more stable. Well-Conditioned Triangle: A triangle is considered well-conditioned when all its interior angles fall within the range of approximately 30° to 120°. This range ensures that no angle has a dangerously small or near-180° sine value. Consequence of Weak Figure: A triangle with a very small angle (e.g., 5°) is a weak figure. Even a 1-second error in that angle can introduce a centimetre-level error in the computed side, degrading the overall accuracy of the control network.
Question Type
short_answer
Answer Structure
- Define strength of figure — error amplification concept [1 mark]
- Explain why sine function behavior at small angles causes weakness [1 mark]
- State the well-conditioned angular range 30°–120° and consequence of violating it [1 mark]
Scoring Breakdown
Marks
1
Criteria
Correct definition: strength of figure relates how angular errors amplify into side-length errors
Marks
1
Criteria
Explanation tied to sine function behavior — small angle → rapidly changing sine → large computed error
Marks
1
Criteria
States the 30°–120° range as the criterion for a well-conditioned triangle
Common Mark Deductions
- Stating the range as 60°–90° only — this is too narrow and omits the full acceptable range
- Saying weak triangles are 'bad' without explaining the sine-function mechanism
- Omitting the definition and jumping straight to the range — losing the definition mark
Key Phrases To Include
- strength of figure
- error amplification
- sine function
- 30° to 120°
- well-conditioned
- Law of Sines
In a triangulation network, a baseline PQ = 10 200 m is measured. In triangle PQR, angle P = 55° and angle Q = 68°. In triangle QRS, angle Q = 48° and angle S = 65°. The common side is QR. (a) Compute the length of side QR. (b) Using QR as a new baseline, compute side RS. [3 marks]
Marks
3
Topic
Triangulation — Extended Chain Computation
Difficulty
medium
Template Id
T8
Examiner Tip
In multi-triangle problems, always explicitly label which angle is opposite which side before writing the ratio. This prevents the most common pairing error.
Model Answer
Given: PQ = 10 200 m, ∠P = 55°, ∠Q = 68° (in △PQR); ∠Q' = 48°, ∠S = 65° (in △QRS) Part (a) — Compute QR: Step 1: ∠R (in △PQR) = 180° − 55° − 68° = 57° Step 2: QR is opposite ∠P; PQ is opposite ∠R QR / sin P = PQ / sin R QR = PQ × (sin P / sin R) QR = 10 200 × (sin 55° / sin 57°) QR = 10 200 × (0.81915 / 0.83867) QR = 10 200 × 0.97672 QR ≈ 9 963 m Part (b) — Compute RS using QR as new baseline: Step 1: ∠R' (in △QRS) = 180° − 48° − 65° = 67° Step 2: RS is opposite ∠Q'; QR is opposite ∠S RS / sin Q' = QR / sin S RS = QR × (sin Q' / sin S) RS = 9 963 × (sin 48° / sin 65°) RS = 9 963 × (0.74314 / 0.90631) RS = 9 963 × 0.81994 RS ≈ 8 169 m
Question Type
numerical
Answer Structure
- Part (a) Step 1: Angle sum check for △PQR, find ∠R [½ mark]
- Part (a) Step 2: Correct Law of Sines for QR, numerical answer [1 mark]
- Part (b) Step 1: Angle sum check for △QRS, find ∠R' [½ mark]
- Part (b) Step 2: Correct Law of Sines for RS using QR, numerical answer [1 mark]
Scoring Breakdown
Marks
1
Criteria
Correctly computes ∠R = 57° and arrives at QR ≈ 9 963 m with correct opposite-angle pairing
Marks
1
Criteria
Correctly computes ∠R' = 67° in the second triangle
Marks
1
Criteria
Correctly applies Law of Sines to find RS ≈ 8 169 m using QR as the new baseline
Common Mark Deductions
- Carrying an uncorrected angle into Part (b) — errors propagate, losing both marks
- Wrong opposite angle pairing (QR opposite ∠Q instead of ∠P)
- Not identifying QR as the baseline for the second triangle
Key Phrases To Include
- 180° − angles = third angle
- opposite angle pairing
- Law of Sines
- new baseline
A triangle in a triangulation network has angles of 15°, 20°, and 145°. Comment on the suitability of this triangle as a triangulation figure, explaining the geometric and computational reasons. [3 marks]
Marks
3
Topic
Triangulation — Strength of Figure Assessment
Difficulty
medium
Template Id
T9
Examiner Tip
For 'comment on suitability' questions, use a three-part structure: (1) criterion check, (2) mathematical reason, (3) conclusion with recommendation. This ensures you address all marking points.
Model Answer
Assessment of Suitability: This triangle is unsuitable as a triangulation figure for the following reasons: 1. Violation of Well-Conditioned Range: Two of the three angles (15° and 20°) fall below the minimum recommended angle of 30° for a well-conditioned triangulation figure. Only angles in the range 30°–120° produce reliable computed sides. 2. Sine Function Sensitivity at Small Angles: • sin 15° = 0.2588 and sin 20° = 0.3420 — both small values. • At these small angles, the sine function changes rapidly; a 1-second error in the 15° angle produces a much larger proportional change in sin 15° than the same 1-second error near 60°. • By the Law of Sines, the computed side = baseline × (sin small angle / sin opposite angle), so the error in the numerator is disproportionately large. 3. Elongated Shape: The 145° angle produces a very flat, elongated triangle. The side opposite 145° (the largest side) is well-determined, but the two short sides opposite 15° and 20° are very poorly determined. Conclusion: All three angles violate the 30°–120° range criterion. This triangle has very poor strength of figure and should be redesigned with better-conditioned angles.
Question Type
short_answer
Answer Structure
- Identify violation of the 30°–120° range criterion [1 mark]
- Explain the sine function sensitivity mechanism at small angles [1 mark]
- Describe the physical/geometric consequence (elongated shape, poor side determination) [1 mark]
Scoring Breakdown
Marks
1
Criteria
States that two angles are below 30°, violating the well-conditioned triangle criterion
Marks
1
Criteria
Explains the rapidly-changing sine at small angles and its effect via the Law of Sines
Marks
1
Criteria
Addresses the 145° angle, elongated shape, and concludes with a recommendation
Common Mark Deductions
- Simply saying 'the triangle is weak' without explaining why (no mechanism = no mark)
- Only mentioning the two small angles without discussing the 145° angle
- Not making a conclusion or recommendation
Key Phrases To Include
- well-conditioned range 30°–120°
- sine function changes rapidly
- strength of figure
- error amplification
- Law of Sines
Enumerate and briefly describe the three primary methods of establishing horizontal control. For each method, state the primary field measurement taken. [3 marks]
Marks
3
Topic
Horizontal Control — Classification of Methods
Difficulty
easy
Template Id
T10
Examiner Tip
Number each method clearly and maintain the same structure for each (name → measurement → brief description). Examiners match your answer against a key — parallel structure helps them award every mark you earned.
Model Answer
Three Primary Methods of Horizontal Control: 1. Triangulation: Primary field measurement: All interior angles of a network of triangles, plus at least one measured baseline. Description: A series of connected triangles are formed across the survey area. The angles of each triangle are measured precisely with a theodolite, and the unknown sides are computed using the Law of Sines. 2. Trilateration: Primary field measurement: All side lengths of the triangle network, measured by electronic distance measurement (EDM). Description: Instead of angles, all distances are measured directly. Triangle angles are then computed using the Law of Cosines. This became prominent with the development of precision EDM instruments. 3. Traverse: Primary field measurement: Horizontal angles (or directions) at each traverse station AND the distance of each traverse leg. Description: A series of connected lines is run through the survey area, with both the direction and length of each line measured. Traverses may be open (between two known control points) or closed (looping back to the starting point or closing on a known point).
Question Type
short_answer
Answer Structure
- Method 1 — Triangulation: name + primary measurement (angles + baseline) + brief description [1 mark]
- Method 2 — Trilateration: name + primary measurement (all distances by EDM) + brief description [1 mark]
- Method 3 — Traverse: name + primary measurement (angles AND distances) + brief description [1 mark]
Scoring Breakdown
Marks
1
Criteria
Triangulation correctly described with angles + baseline as primary measurement
Marks
1
Criteria
Trilateration correctly described with all side distances (EDM) as primary measurement
Marks
1
Criteria
Traverse correctly described with BOTH angles and distances as primary measurements
Common Mark Deductions
- Stating that traverse measures only directions without distances (or vice versa) — both are required
- Listing GNSS as one of the three classical methods without describing the three traditional methods
- Describing all three methods in one combined paragraph making it unclear which is which
Key Phrases To Include
- triangulation
- trilateration
- traverse
- angles
- baseline
- EDM
- Law of Sines
- Law of Cosines
Discuss the classification of geodetic control networks by order of accuracy. Include in your answer: (a) the general hierarchy, (b) the principle governing the extension of lower-order from higher-order control, (c) the application of leveling misclosure tolerances by order, and (d) the role of NAMRIA in the Philippine context. [5 marks]
Marks
5
Topic
Orders of Accuracy — Philippine Context
Difficulty
hard
Template Id
T11
Examiner Tip
Five-mark questions are marked against a point-by-point breakdown. Structure your answer with clear part labels (a), (b), (c), (d) matching the question. Never write a single continuous paragraph for a 5-mark question — subdivided answers let the examiner award every mark you earned.
Model Answer
Classification of Geodetic Control Networks by Order of Accuracy (a) General Hierarchy: Geodetic control networks in the Philippines are classified into orders of decreasing accuracy: • First Order (Geodetic): Highest precision; forms the national primary framework. Spacing: 100–300 km (horizontal); used for crustal deformation monitoring, national mapping datum. • Second Order (Class I and II): Secondary framework densifying First Order; spacing 20–50 km. Sufficient for state/regional mapping and major engineering projects. • Third Order: Local control for cadastral surveys, engineering, and construction projects. Spacing 2–10 km. Each lower order is established by measurements made relative to the immediately superior order, never independently. (b) Principle of Extension (Whole to Part): The cardinal principle is: control networks are always densified from a higher order to a lower order — from the whole to the part. A Third Order point is established by measuring from Second Order points; a Second Order point is established from First Order points. It is never permissible to extend a higher-order network from lower-order monuments because the accumulated errors of the lower-order points would corrupt the higher-order framework. This also ensures national consistency and traceability. (c) Leveling Misclosure Tolerances by Order: Precision leveling is used to establish vertical control benchmarks. The allowable misclosure T for a leveling circuit is computed as: T = k√K where K = total loop distance in kilometres and k is an order-dependent constant: • First Order, Class I: k = 4 mm • First Order, Class II: k = 6 mm • Second Order: k = 8 mm • Third Order: k = 12 mm For example, a Second Order loop of 16 km has an allowable misclosure of: T = 8√16 = 8 × 4 = 32 mm. If the actual misclosure exceeds T, the leveling run must be repeated. (d) Role of NAMRIA in the Philippine Context: The National Mapping and Resource Information Authority (NAMRIA), under the Department of Environment and Natural Resources (DENR), is the central mapping agency of the Republic of the Philippines. NAMRIA: • Maintains and publishes the Philippine Reference System of 1992 (PRS92), which is the official horizontal datum tied to WGS84. • Publishes the Philippine Vertical Datum (mean sea level at Intramuros tide gauge) as the national height reference. • Classifies, maintains, and publishes the national geodetic control network monuments. • Issues certificates of geodetic control data to licensed geodetic engineers for survey tie-in, as required by RA 8560 (Geodetic Engineers Act) and PD 1529 (Property Registration Decree). • Coordinates with the PPCP (Philippine Persistent CORS Project) for GNSS-based active control network densification.
Question Type
long_answer
Answer Structure
- Part (a): Hierarchy with three orders named, brief description of each, and spacing/use [1 mark]
- Part (b): Whole-to-part principle explained with direction and prohibition stated [1 mark]
- Part (c): Formula T = k√K stated and applied with correct k values for at least two orders [1.5 marks]
- Part (d): NAMRIA role — PRS92, datum, control network, RA 8560/PD 1529 reference [1.5 marks]
Scoring Breakdown
Marks
1
Criteria
Correct three-tier hierarchy (First, Second, Third Order) with distinguishing features of each
Marks
1
Criteria
Correct whole-to-part principle including the prohibition on extending higher-order from lower-order
Marks
1
Criteria
Correct formula T = k√K with at least two correct k values for different orders, and a worked example
Marks
1
Criteria
NAMRIA identified as the Philippine national mapping authority responsible for datum and control network
Marks
1
Criteria
Reference to PRS92, WGS84 tie-in, relevant Philippine law (RA 8560 or PD 1529), and modern GNSS control
Common Mark Deductions
- Omitting the worked numerical example for the tolerance formula — examiners expect application, not just the formula
- Mentioning NAMRIA without specifying its role in PRS92 or the national control network
- Not referencing any Philippine law — this is a PRC board exam; legal references earn marks
- Describing the hierarchy in reverse order (Third → First) showing conceptual confusion
Key Phrases To Include
- First Order
- Second Order
- Third Order
- whole to the part
- T = k√K
- NAMRIA
- PRS92
- WGS84
- RA 8560
- PD 1529
- densification
A triangulation network is established to control a topographic mapping survey of a Philippine municipality. Baseline AB = 12 400 m is precisely measured. In triangle ABC, angle A = 48°30' and angle B = 63°15'. In triangle ACD, diagonal AC is the common side, angle A = 37°45', and angle C = 72°20'. (a) Compute side AC. (b) Compute side CD. (c) Assess whether triangle ACD is well-conditioned. [5 marks]
Marks
5
Topic
Triangulation — Extended Chain with DMS Angles
Difficulty
hard
Template Id
T12
Examiner Tip
DMS-to-decimal conversion is a hidden mark trap. Write the conversion explicitly: 63°15' = 63 + 15/60 = 63.25°. Examiners see this and know you understand the process. Skipping it suggests guessing.
Model Answer
Given: AB = 12 400 m △ABC: ∠A = 48°30', ∠B = 63°15' △ACD: ∠A = 37°45', ∠C = 72°20' Part (a) — Compute AC (in △ABC): Step 1: ∠C = 180°00' − 48°30' − 63°15' = 68°15' Step 2: AC is opposite ∠B; AB is opposite ∠C AC / sin B = AB / sin C AC = 12 400 × (sin 63°15' / sin 68°15') sin 63°15' = sin(63 + 15/60)° = sin 63.25° = 0.89253 sin 68°15' = sin(68 + 15/60)° = sin 68.25° = 0.92978 AC = 12 400 × (0.89253 / 0.92978) AC = 12 400 × 0.95994 AC ≈ 11 903 m Part (b) — Compute CD (in △ACD, using AC = 11 903 m as new baseline): Step 1: ∠D = 180°00' − 37°45' − 72°20' = 69°55' Step 2: CD is opposite ∠A; AC is opposite ∠D CD / sin A = AC / sin D CD = 11 903 × (sin 37°45' / sin 69°55') sin 37°45' = sin 37.75° = 0.61280 sin 69°55' = sin 69.917° = 0.93906 CD = 11 903 × (0.61280 / 0.93906) CD = 11 903 × 0.65256 CD ≈ 7 767 m Part (c) — Assessment of triangle ACD: Angles: ∠A = 37°45' (37.75°), ∠C = 72°20' (72.33°), ∠D = 69°55' (69.92°) All three angles fall within the well-conditioned range of 30°–120°. Verdict: Triangle ACD is well-conditioned. No angle is below 30° or above 120°, ensuring reliable Law of Sines computation with minimal error amplification. The figure has good strength of figure.
Question Type
numerical
Answer Structure
- Part (a) Step 1: ∠C = 68°15' by angle sum [½ mark]
- Part (a) Step 2: Correct Law of Sines, AC ≈ 11 903 m with units [1 mark]
- Part (b) Step 1: ∠D = 69°55' by angle sum [½ mark]
- Part (b) Step 2: Correct Law of Sines using AC as new baseline, CD ≈ 7 767 m [1 mark]
- Part (c): Check all three angles against 30°–120° range, explicit verdict [1 mark — accept reasonable computed values ± rounding]
Scoring Breakdown
Marks
1
Criteria
Angle sum for △ABC and correct AC computation with proper opposite-angle pairing
Marks
1
Criteria
Angle sum for △ACD and correct CD computation using AC as the new baseline
Marks
1
Criteria
Correct conversion of DMS angles to decimal degrees for sine computation
Marks
1
Criteria
Correct chain: AC from △ABC carried forward as baseline for △ACD
Marks
1
Criteria
Correct assessment of △ACD: all angles in 30°–120° range → well-conditioned with explanation
Common Mark Deductions
- Not converting DMS to decimal degrees before computing sine values — major source of error
- Using the wrong opposite angle (e.g., pairing AC opposite ∠A instead of ∠B in △ABC)
- Not clearly stating that AC becomes the new baseline for the second triangle
- Assessing only one or two angles for well-conditioned criterion instead of all three
- Rounding errors from premature truncation of sine values — carry at least 5 decimal places
Key Phrases To Include
- angle sum = 180°
- DMS to decimal conversion
- opposite angle pairing
- new baseline
- well-conditioned
- 30°–120°
- strength of figure
Explain the role of a baseline in a triangulation survey. Why must the baseline be measured with the highest possible precision? [2 marks]
Marks
2
Topic
Triangulation — Role of the Baseline
Difficulty
medium
Template Id
T13
Examiner Tip
The second mark is specifically for the error propagation argument. Make this mechanism explicit: 'All computed sides inherit the baseline error because they are computed as ratios involving the baseline.'
Model Answer
Role of the Baseline: The baseline is the only directly measured distance in a classical triangulation survey. It provides the scale of the entire network — without it, only the shape (angles) of the triangles is known but no actual distances can be computed. All computed sides in the network ultimately derive their length from the ratio with the baseline via the Law of Sines. Why Maximum Precision is Required: Because all other distances in the network are computed as proportional multiples of the baseline, any error in the baseline length propagates into EVERY computed side in the network. A 1-part-per-million (1 ppm) error in the baseline introduces a 1 ppm systematic error in all derived distances throughout the chain. Since the baseline error cannot be removed by angular adjustment, it must be minimized at the source by using precision tapes (invar tapes with tension and temperature corrections) or modern precise EDM with atmospheric corrections.
Question Type
short_answer
Answer Structure
- Part 1: Role — baseline provides scale; all computed sides derive from it via Law of Sines [1 mark]
- Part 2: Reason for precision — baseline error propagates to ALL computed sides; cannot be removed by adjustment [1 mark]
Scoring Breakdown
Marks
1
Criteria
States that the baseline provides the scale of the network and that all other distances are computed from it
Marks
1
Criteria
Explains that baseline error propagates systematically to all computed sides in the network
Common Mark Deductions
- Saying 'the baseline is important for accuracy' without explaining the propagation mechanism
- Confusing the baseline with a traverse leg — baseline is specifically for triangulation scale
- Not mentioning that angular adjustment cannot correct baseline errors
Key Phrases To Include
- scale of the network
- only directly measured distance
- Law of Sines
- error propagates
- all computed sides
- invar tape
- ppm
State the leveling misclosure formula and compute the allowable misclosure for a first-order class I level loop of 36 km. State whether an observed misclosure of 18 mm is acceptable. [2 marks]
Marks
2
Topic
Vertical Control — Leveling Tolerance by Order
Difficulty
easy
Template Id
T14
Examiner Tip
Always write the verdict explicitly: 'Since [observed] < [tolerance], the run is ACCEPTABLE.' Examiners will not infer this from numbers alone — the stated conclusion earns the mark.
Model Answer
Formula: T = k√K where K = loop distance in km, k = 4 mm (First Order, Class I) Computation: T = 4 × √36 T = 4 × 6 T = 24 mm Acceptability Check: Observed misclosure = 18 mm Allowable tolerance T = 24 mm Since 18 mm < 24 mm, the observed misclosure is ACCEPTABLE. The leveling run meets First Order, Class I precision.
Question Type
numerical
Answer Structure
- State T = k√K with k = 4 mm for First Order Class I [½ mark]
- Compute T = 24 mm correctly [½ mark]
- Compare 18 mm vs. 24 mm and make an explicit verdict [1 mark]
Scoring Breakdown
Marks
1
Criteria
Correctly identifies k = 4 mm for First Order Class I and computes T = 24 mm
Marks
1
Criteria
Makes a correct and explicit comparison (18 mm < 24 mm) and states that the misclosure is acceptable
Common Mark Deductions
- Using k = 8 mm (Second Order) for a First Order question
- Computing T = 4 × 36 = 144 mm (forgetting the square root)
- Failing to state the acceptability verdict — the comparison is worth a full mark
Key Phrases To Include
- T = k√K
- k = 4 mm
- First Order Class I
- T = 24 mm
- 18 mm < 24 mm
- acceptable
Under Philippine law, why must cadastral and land registration surveys be tied to the national geodetic control network? Reference at least two relevant laws in your answer. [2 marks]
Marks
2
Topic
Philippine Geodetic Law — Control Network Requirements
Difficulty
medium
Template Id
T15
Examiner Tip
Board exams regularly test knowledge of Philippine geodetic legislation. Always connect the law to the specific technical requirement it mandates. 'PD 1529 requires tie-in' earns a mark; 'a law requires tie-in' earns nothing.
Model Answer
Cadastral and land registration surveys in the Philippines must be tied to the national geodetic control network for two principal reasons: 1. Legal Requirement and Survey Accuracy: Under Presidential Decree No. 1529 (Property Registration Decree), all surveys submitted for land registration must comply with Bureau of Lands (now DENR-LMB) technical standards. Tie-in to NAMRIA-published geodetic control ensures that parcel boundaries are uniquely and unambiguously positioned within the national coordinate reference system (PRS92/PPCS), preventing overlapping claims and positional discrepancies. 2. Professional Standards and Responsibility: Under Republic Act No. 8560 (Philippine Geodetic Engineering Act of 1998), it is the duty of a licensed geodetic engineer to perform surveys in accordance with technical and professional standards. Using the national geodetic control network ensures traceability of all measurements to a common datum (PRS92), which is a fundamental requirement of professional geodetic practice. Failure to tie-in to the control network is a basis for disapproval of the survey by DENR-LMB.
Question Type
short_answer
Answer Structure
- Legal requirement — PD 1529 reference with explanation of purpose (unique parcel positioning, PRS92) [1 mark]
- Professional standard — RA 8560 reference with explanation of geodetic engineer's duty and datum traceability [1 mark]
Scoring Breakdown
Marks
1
Criteria
Correctly references PD 1529 and explains it requires surveys to be tied to national control for registration
Marks
1
Criteria
Correctly references RA 8560 and explains the geodetic engineer's obligation to use national datum (PRS92)
Common Mark Deductions
- Mentioning laws by number only without explaining their relevance to the control tie-in requirement
- Citing CA 141 (Public Land Act) as the primary law — while relevant, PD 1529 and RA 8560 are more directly applicable here
- General answer about 'accuracy' without connecting to the legal mandate
Key Phrases To Include
- PD 1529
- Property Registration Decree
- RA 8560
- Geodetic Engineering Act
- PRS92
- NAMRIA
- datum traceability
- DENR-LMB
Mark Wise Strategy
Dos
- Start directly with the answer — no preamble like 'The answer is...'
- Use the exact technical term from the question (e.g., 'triangulation,' 'baseline,' 'strength of figure')
- For definition questions, include what is measured AND how it is used
- For formula questions, write the formula with all variables defined
- For concept questions, include one distinguishing characteristic
Donts
- Do not write a full paragraph — you have no time and gain no marks
- Do not leave it as a single word — 'angles' alone is incomplete
- Do not confuse triangulation (angles) with trilateration (distances)
Marks
1
Strategy
Write one complete, technically precise sentence. Include the key term, the defining property, and where applicable, the formula. Do not write more than three lines — you waste time that could earn marks elsewhere.
Expected Length
1–3 lines (one complete, precise sentence or equation)
Time Allocation
1–2 minutes
Dos
- Separate the two mark-earning points visually (numbering or new line)
- For numerical: always show the formula before substituting values
- For comparison questions: address both items being compared using the same criterion
- State units on all final numerical answers
- Write the verdict explicitly for tolerance problems (e.g., 'acceptable/not acceptable')
Donts
- Do not write only one point and expect to earn both marks
- Do not skip the formula step in numericals — partial credit requires it
- Do not use T = k × K (linear) — always T = k√K for leveling misclosure
Marks
2
Strategy
Two marks = two distinct earning points. Identify them from the question (compare, compute two steps, give definition + application). Write one clear point per 'mark unit.' For numericals, write: Given → Formula → Substitution → Answer.
Expected Length
3–6 lines (two distinct, developed points or a short worked computation)
Time Allocation
3–5 minutes
Dos
- Explicitly number or label each of the three points
- For triangulation computations: Step 1 = angle sum, Step 2 = Law of Sines setup, Step 3 = numerical answer
- For concept questions: definition → mechanism (why/how) → application/consequence
- Convert DMS to decimal degrees explicitly and show the conversion
- State the conclusion sentence at the end of concept answers
Donts
- Do not write a single continuous paragraph — it hides your three points and costs marks
- Do not assume the examiner will infer your intended point — state it directly
- Do not omit the strength-of-figure range (30°–120°) when asked to assess a triangle
Marks
3
Strategy
Three marks = three distinct earning points, usually covering definition + mechanism + application/example, or three computational steps. Use numbered or bulleted sub-answers. For complex computations, box intermediate answers (e.g., ∠C = 57°) to signal checkpoints to the examiner.
Expected Length
Half a page or a complete multi-step computation (8–12 lines)
Time Allocation
6–9 minutes
Dos
- Use labeled sub-sections matching the question's lettered parts
- Include a worked numerical example even if not explicitly required — it demonstrates mastery
- Reference PRS92 and NAMRIA for Philippine-context questions
- Cite RA 8560 or PD 1529 when the question involves professional practice or land registration
- End each sub-part with a brief concluding sentence
- Use tables or parallel lists for comparison questions to maximize clarity
Donts
- Do not write one long unstructured paragraph — markers cannot identify your five earning points
- Do not omit the Philippine legal/institutional context when the question involves professional practice
- Do not spend more than 18 minutes — learn to write concise but complete answers
- Do not leave any sub-part blank — attempt all parts, even briefly, to earn partial credit
Marks
5
Strategy
Five-mark questions are multi-part or require full analysis. Treat each sub-part as an independent mark opportunity. Use part labels (a), (b), (c) matching the question. Include at least one worked numerical example for any formula-based discussion. Reference Philippine laws and standards (PRS92, NAMRIA, RA 8560, PD 1529) where the context supports it — this signals professional-level knowledge that examiners reward.
Expected Length
Full page — comprehensive multi-part answer (20–35 lines)
Time Allocation
12–18 minutes
General Answer Writing Tips
- Always begin concept questions with a crisp, one-sentence definition using the exact technical term (e.g., 'Triangulation is a method of horizontal control surveying in which all angles of a chain of triangles are measured and one or more baselines are measured to compute unknown sides using the Law of Sines.').
- For numerical problems, write out the given data, the formula, the substitution, and the final answer with units — examiners award partial credit at each step, so never skip steps even if the arithmetic seems obvious.
- Always verify the angle sum equals 180° before applying the Law of Sines in any triangulation problem; state this check explicitly ('Angle C = 180° − A − B') to earn the verification mark.
- Use the leveling tolerance formula exactly as T = k√K, identifying the constant k and the loop distance K in km before substituting — failure to show this setup costs marks.
- When the question asks you to compare two methods (e.g., triangulation vs. trilateration), use a parallel two-column structure: one column per method, same rows for each comparison criterion — this signals organized thinking to the examiner.
- Reference the correct Philippine legal framework where relevant: RA 8560 (PRC Modernization Act, governing professional practice), PD 1529 (Property Registration Decree, requiring cadastral surveys tied to control networks), and the NAMRIA classification of control orders.
- For diagram-based questions, always label ALL parts: points, angles, sides, baselines, known vs. unknown quantities — an unlabeled diagram earns zero diagram marks even if the computation is correct.
- In strength-of-figure questions, always state WHY a weak triangle is weak: 'A small angle (< 30°) has a rapidly changing sine value, so a small angular measurement error propagates into a large error in the computed side length.'
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