Question

select the correct answer. an observatory is 150 feet high. when a person is standing in the observatory looking at an island, the angle of depression is 25°. what is the approximate horizontal distance from the observatory to the island? observatory 150 ft island a. 70 feet b. 355 feet c. 322 feet d. 166 feet

Explanation:

Step1: Identify trigonometric ratio

We use $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta=25^\circ$, opposite side $=150$ ft, adjacent side $=x$ (horizontal distance we need to find). Rearranged, $x = \frac{150}{\tan(25^\circ)}$.

Step2: Calculate $\tan(25^\circ)$

$\tan(25^\circ) \approx 0.4663$

Step3: Compute horizontal distance

$x \approx \frac{150}{0.4663}$

Answer:

C. 322 feet