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?
image of a right triangle with observatory at the top right vertex, island at the bottom left vertex, right angle at the bottom right vertex, height of 150 ft, angle of 25° at the island vertex and at the observatory vertex (between the horizontal dashed line and the hypotenuse)
options:
a. 322 feet
b. 186 feet
c. 70 feet
d. 355 feet

Explanation:

Step1: Define variables

Let $x$ = horizontal distance.

Step2: Use tangent function

$\tan(25^\circ) = \frac{150}{x}$

Step3: Solve for x

$x = \frac{150}{\tan(25^\circ)}$

Step4: Calculate value

$\tan(25^\circ) \approx 0.4663$, so $x \approx \frac{150}{0.4663} \approx 322$ feet.

Answer:

A. 322 feet