Question

A mountain climber at the top of the mountain 160 metres above ground level observes the angle of depression of the two cars parked on the road side at 60 degree (second car) and 30degree (first car) respectively. Find the distance : 1. from the base of the mountain to the first car, 2. from the base of the mountain to the second car and, 3. between the two cars.​

Answer 1

a. distance between the base of the mountain and the first car, d = 277 m

b. distance between the base of the mountain and the second car, s = 92 m

c. distance between the two cars = 185 m

Explanation:

a. Since the angle of depression is 30°, the interior angle = (90 - 30)° = 60°

Let the distance between the base of the mountain and the first car be d, and height of the mountain = 160 m

tan 60° = d/160 m

d = tan 60° * 160 m

distance between the base of the mountain and the first car, d = 277 m

b. Since the angle of depression is 60°, the interior angle = (90 - 60)° = 30°

Let the distance between the base of the mountain and the second car be s, and height of the mountain = 160 m

tan 30° = s/160 m

s = tan 30° * 160 m

distance between the base of the mountain and the second car, s = 92 m

c. distance between the two cars = 277 - 92

distance between the two cars = 185 m