CST Survey Calculations & Coordinate Systems 2 — Questions and Answers
Question 1: A traverse course has a bearing of N 30°00' E and a length of 200.00 ft. What is its latitude?
- +115.47 ft
- +100.00 ft
- +200.00 ft
- +173.21 ft (Correct answer)
Correct answer: +173.21 ft
Latitude = distance × cos(bearing) = 200 × cos 30° = 173.21 ft, positive because it runs north.
Question 2: What is the departure of a course bearing S 45°00' W with a length of 100.00 ft?
- -50.00 ft
- -100.00 ft
- -70.71 ft (Correct answer)
- +70.71 ft
Correct answer: -70.71 ft
Departure = 100 × sin 45° = 70.71 ft, negative because the course runs west.
Question 3: A closed traverse has a latitude misclosure of 0.30 ft and a departure misclosure of 0.40 ft. What is the linear error of closure?
- 0.70 ft
- 0.35 ft
- 0.10 ft
- 0.50 ft (Correct answer)
Correct answer: 0.50 ft
Linear error = √(0.30² + 0.40²) = 0.50 ft.
Question 4: A traverse with a perimeter of 5,000 ft has a linear error of closure of 0.50 ft. What is its relative precision?
- 1:2,500
- 1:5,000
- 1:10,000 (Correct answer)
- 1:25,000
Correct answer: 1:10,000
Relative precision = 0.50 / 5,000 = 1/10,000.
Question 5: Under the compass (Bowditch) rule, how is the latitude correction for each course found?
- In proportion to the course's latitude divided by the sum of all absolute latitudes
- Split equally among all courses
- In proportion to the angle measured at each station
- In proportion to the course length divided by the total perimeter (Correct answer)
Correct answer: In proportion to the course length divided by the total perimeter
The compass rule spreads the misclosure in proportion to each course's length relative to the total traverse length.
Question 6: What should the interior angles of a closed six-sided traverse add up to?
- 540°
- 900°
- 1080°
- 720° (Correct answer)
Correct answer: 720°
Sum of interior angles = (n − 2) × 180° = 4 × 180° = 720°.
Question 7: Which bearing matches an azimuth of 225° (measured from north)?
- S 45° E
- N 45° W
- S 45° W (Correct answer)
- N 45° E
Correct answer: S 45° W
225° lies in the southwest quadrant, and 225° − 180° = 45°, so the bearing is S 45° W.
CST Survey Calculations & Coordinate Systems 2
A traverse course has a bearing of N 30°00' E and a length of 200.00 ft.
What is its latitude?