LSIT Mathematics for Surveying 3 — Questions and Answers
Question 1: A slope distance of 542.30 ft is measured on a grade of 3.75%. What is the horizontal distance?
- 541.91 ft (Correct answer)
- 540.12 ft
- 542.68 ft
- 538.47 ft
Correct answer: 541.91 ft
Horizontal distance = slope distance × cos(arctan(0.0375)) ≈ 542.30 × 0.99930 ≈ 541.91 ft.
Question 2: The interior angles of a closed five-sided traverse sum to 540°. If four measured angles are 98°14', 112°33', 87°47', and 125°06', what is the fifth angle (assuming no angular error)?
- 116°20' (Correct answer)
- 115°20'
- 116°40'
- 117°20'
Correct answer: 116°20'
Sum of four angles = 423°40'; fifth angle = 540°00' − 423°40' = 116°20'.
Question 3: Using the coordinate method, a triangle has vertices at (0,0), (6,0), and (3,4). What is its area in square units?
- 12 (Correct answer)
- 10
- 14
- 8
Correct answer: 12
Area = ½|x₁(y₂−y₃)+x₂(y₃−y₁)+x₃(y₁−y₂)| = ½|0(0−4)+6(4−0)+3(0−0)| = ½×24 = 12.
Question 4: A surveyor needs to convert 45°27'36" to decimal degrees. What is the result?
- 45.460° (Correct answer)
- 45.463°
- 45.456°
- 45.476°
Correct answer: 45.460°
27'/60 = 0.450°; 36"/3600 = 0.010°; total = 45 + 0.450 + 0.010 = 45.460°.
Question 5: A circular curve has a radius of 800 ft and a central angle (Δ) of 24°30'. What is the arc length?
- 341.75 ft (Correct answer)
- 325.40 ft
- 352.00 ft
- 336.90 ft
Correct answer: 341.75 ft
Arc length = R × Δ (radians) = 800 × (24.5° × π/180) = 800 × 0.42760 ≈ 341.75 ft.
Question 6: In a right triangle used for a surveying calculation, the opposite side is 45.0 ft and the hypotenuse is 75.0 ft. What is the angle opposite the 45.0 ft side?
- 36°52' (Correct answer)
- 37°00'
- 53°08'
- 36°00'
Correct answer: 36°52'
sin θ = 45/75 = 0.6000; θ = arcsin(0.6000) = 36°52'.
Question 7: A parcel of land is described as the SW¼ of the NE¼ of a section. How many acres does it contain?
- 40 acres (Correct answer)
- 80 acres
- 20 acres
- 160 acres
Correct answer: 40 acres
A full section is 640 acres; ¼ × ¼ = 1/16; 640/16 = 40 acres.
LSIT Mathematics for Surveying 3
A slope distance of 542.30 ft is measured on a grade of 3.75%.
What is the horizontal distance?