Question

a helicopter hovers 650 feet above a small island. the figure shows that the angle of depression from the helicopter to point p is $31^{\circ}$. how far off the coast to the nearest foot, is the island?
(1 point)
○ 391 ft.
○ 557 ft.
○ 1082 ft.
○ 335 ft.

Explanation:

Step1: Identify tangent relationship

The angle of depression equals the angle at point P, so $\tan(31^\circ) = \frac{650}{d}$.

Step2: Rearrange to solve for $d$

$d = \frac{650}{\tan(31^\circ)}$

Step3: Calculate the value

$\tan(31^\circ) \approx 0.6009$, so $d \approx \frac{650}{0.6009} \approx 1082$

Answer:

1082 ft.