Question

Please help.

a helicopter hovers 1400 feet above a small island. the figure shows that the angle of the depression from the to the point P is 30 degrees. how far off the coast, to the nearest foot, is the island?

Answer 1

Explanation:

this (outside) angle of depression is equal to the inner angle at P.

because the line of sight from the helicopter to P is like the diagonal in a rectangle spring the rectangle into 2 equal right-angled triangles (one of just rotated by 180° of the other).

so, the angle at P is 30°.

1400 ft = sin(30)×radius

radius being the line of sight from the helicopter to P.

we need to calculate the radius, because we need it for d :

d = cos(30)×radius

radius = 1400/sin(30) = 2800 ft

d = cos(30)×2800 = 2,424.871131... ft ≈ 2,425 ft