Question

A rescue team is 700 ft. away from a vertical cliff. The team measures the angle of elevation to the top of the cliff as 65°. A climber is stranded on the cliff at an angle of elevation of 40°. How far is the climber from the top of the cliff?(1 point)
Responses

The climber is 1,501.15 ft. from the top of the cliff.
The climber is 1,501.15 ft. from the top of the cliff.

The climber is 913.78 ft. from the top of the cliff.
The climber is 913.78 ft. from the top of the cliff.

The climber is 587.37 ft. from the top of the cliff.
The climber is 587.37 ft. from the top of the cliff.

The climber is 326.42 ft. from the top of the cliff.
The climber is 326.42 ft. from the top of the cliff.

Answer 1

Let the horizontal distance from the team to the cliff base be 700 ft. Heights above the base:
top: h1 = 700·tan(65°)
climber: h2 = 700·tan(40°)

Distance between them: h1 − h2 = 700[ tan(65°) − tan(40°) ] ≈ 700(2.1445069 − 0.8390996) ≈ 913.78 ft.

So the climber is about 913.78 ft from the top of the cliff.