Question

a helicopter hovers 1125 feet above a small island. the figure shows that the angle of depression from the helicopter to point p on the coast is 35°. how far off the coast, to the nearest foot, is the island? the island is approximately feet off the coast. (simplify your answer. round to the nearest whole number as needed.)

Explanation:

Step1: Identify the trig - ratio

We have a right - triangle where the height of the helicopter above the island (opposite side to the angle of depression) is 1125 feet and we want to find the distance from the island to the point on the coast (adjacent side to the angle of depression). We use the tangent function since $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.
$\tan(35^{\circ})=\frac{1125}{d}$

Step2: Solve for $d$

We can rewrite the equation as $d = \frac{1125}{\tan(35^{\circ})}$.
We know that $\tan(35^{\circ})\approx0.7002$.
So, $d=\frac{1125}{0.7002}\approx1607$.

Answer:

1607