Question

A helicopter hovers 500 feet above a small island. The figure shows that the angle of

depression from the helicopter
to point P is 49º. How far off
the coast, to the nearest foot, is the island?

Answer 1

435 ft

Explanation:

Reference angle = <P = 49° (angle of elevation)

Opposite side = 500 ft

Adjacent side = d = ?

Apply trigonometric function, TOA.

This:

Tan P = opp/adj

Tan 49 = 500/d

d × Tan 49 = 500

d = 500/Tan 49

d = 434.643369 ≈ 435 ft (to the nearest foot)