Question

A surveyor is working to determine the gradient of a hill. The surveyor knows the hill starts at an elevation of 1755 feet and peaks at an elevation of 2105 feet. The distance of the hill from the bottom to the top is 910 feet. Select the responses that represent the angle of elevation of the hill (rounded to the nearest degree) and the trigonometric functions of the angle of elevation.

a. Cosθ= 13/5
b. Cosθ= 12/13
c. Cosθ= 13/12
d. Cosθ =13/5

Answer 1

cos∅ = 12 / 13

Hence; Option b) Cosθ= 12/13 is the correct answer

Explanation:

Given the data in the question;

the height( opposite ) = 2105 ft - 1755 ft = 350 ft

the hypotenuse = 910 ft

adjacent = x

as its illustrated in the image uploaded along this answer;

using the Pythagoras theorem

910² = 350² + x²

x² = 828100 - 122500

x² = 705600

x = √705600

x = 840 ft

Now

cos∅ = adjacent / hypotenuse

cos∅ = 840 / 910

we simplify; divide through by 70

cos∅ = 12 / 13

Therefore; Option b) Cosθ= 12/13 is the correct answer