Question

Bob is driving along a straight and level road toward a mountain. At some point on his trip, he measures the angle of elevation to the top of the mountain and finds it to be 21°44'. Find the height of the mountain to the nearest foot if Bob is 13,428.7 feet from the center of the mountain at the base.

A. 5453 ft
B. 5353 ft
C. 53,534 ft
D. 535,342 ft

Answer 1

tan 21 44 = h / 13428.7
h = 13428.7 * tan 21 44

Height = 5353 feet

Answer 2

Option B is the correct answer.

Explanation:

The arrangement is given in the below figure.

We have height of the mountain = x

We also have

`tan(21^044')=(x)/(13428.7)\\x=5352.98ft`

Height of the mountain to the nearest foot = 5353 ft

Option B is the correct answer.