LSIT Mathematics for Surveying 4

Question 1

A traverse leg has a latitude of −312.44 ft and a departure of +184.76 ft. What is the bearing of this leg?

Accepted Answer

S 30°37' E

Answer

Bearing angle = arctan(|departure|/|latitude|) = arctan(184.76/312.44) = 30°37'; negative latitude and positive departure → S 30°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?

Accepted Answer

1:10,000

Answer

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 = 42°, angle B = 67°, and side a (opposite A) = 125.0 ft, what is side b (opposite B)?

Accepted Answer

172.1 ft

Answer

b = a × sin B / sin A = 125.0 × sin 67° / sin 42° = 125.0 × 0.9205 / 0.6691 ≈ 172.1 ft.

Question 4

A vertical curve connects a +2.50% grade and a −1.50% grade. The algebraic difference in grades (A) is:

Accepted Answer

4.00%

Answer

A = g₂ − g₁ = −1.50% − (+2.50%) = −4.00%; 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?

Accepted Answer

152.30 ft

Answer

By convention, the DMD of the first course equals its own departure, which is +152.30 ft.

(LSIT) Land Surveyor in Training Practice Test

(LSIT) Land Surveyor in Training Practice Test

LSIT Mathematics for Surveying 4