LSIT Mathematics for Surveying 4 ā Questions and Answers
Question 1: A traverse leg has a latitude of ā312.44 ft and a departure of +184.76 ft. What is the bearing of this leg?
- S 30Ā°37' E (Correct answer)
- S 59Ā°23' E
- N 30Ā°37' W
- S 30Ā°37' W
Correct answer: S 30Ā°37' E
Bearing angle = arctan(|departure|/|latitude|) = arctan(184.76/312.44) = 30Ā°37'; negative latitude and positive departure ā S 30Ā°37' E.
Question 2: What is the precision ratio of a traverse with a linear misclosure of 0.42 ft and a total traverse length of 4,200 ft?
- 1:10,000 (Correct answer)
- 1:4,200
- 1:8,400
- 1:1,000
Correct answer: 1:10,000
Precision ratio = 1:(total length / misclosure) = 1:(4200/0.42) = 1:10,000.
Question 3: Using the Law of Sines, in triangle ABC where angle A = 42Ā°, angle B = 67Ā°, and side a (opposite A) = 125.0 ft, what is side b (opposite B)?
- 172.1 ft (Correct answer)
- 148.6 ft
- 163.4 ft
- 180.2 ft
Correct answer: 172.1 ft
b = a Ć sin B / sin A = 125.0 Ć sin 67Ā° / sin 42Ā° = 125.0 Ć 0.9205 / 0.6691 ā 172.1 ft.
Question 4: A vertical curve connects a +2.50% grade and a ā1.50% grade. The algebraic difference in grades (A) is:
- 4.00% (Correct answer)
- 1.00%
- ā4.00%
- 2.50%
Correct answer: 4.00%
A = gā ā gā = ā1.50% ā (+2.50%) = ā4.00%; the absolute value |A| = 4.00%.
Question 5: A surveyor computes the area of a closed traverse using the DMD (Double Meridian Distance) method. The DMD of a course equals the DMD of the preceding course, plus the departure of the preceding course, plus the departure of the current course. What is the DMD of the first course if its departure is +152.30 ft?
- 152.30 ft (Correct answer)
- 304.60 ft
- 76.15 ft
- 0.00 ft
Correct answer: 152.30 ft
By convention, the DMD of the first course equals its own departure, which is +152.30 ft.
Question 6: Two points A and B have elevations of 1,245.82 ft and 1,189.37 ft respectively, and a horizontal distance of 830.0 ft. What is the percent grade from A to B?
- ā6.80% (Correct answer)
- +6.80%
- ā5.60%
- +5.60%
Correct answer: ā6.80%
Grade = (elev B ā elev A) / horizontal distance Ć 100 = (1189.37 ā 1245.82) / 830.0 Ć 100 = ā6.80%.
Question 7: A level rod reading of 4.862 ft is taken at a point with a known elevation of 387.541 ft. The instrument height (HI) is:
- 392.403 ft (Correct answer)
- 382.679 ft
- 391.403 ft
- 393.541 ft
Correct answer: 392.403 ft
HI = elevation of point + rod reading = 387.541 + 4.862 = 392.403 ft.
LSIT Mathematics for Surveying 4
A traverse leg has a latitude of ā312.44 ft and a departure of +184.76 ft.
What is the bearing of this leg?