Question

An observatory is 150 feet high. When a person is standing in the observatory looking at an island, the angle of depression is . What is the approximate horizontal distance from the observatory to the island?

A. 70 feet
B. 166 feet
C. 322 feet
D. 355 feet

Answer 1

c.322 ft

Explanation:

took the test

Answer 2

C

Explanation:

We want to find the horizontal distance from the observatory to the island, which is adjacent to the known angle.

Because we also know the height of the observatory and is opposite to the angle, we can consider using tangent. Recall that:

`\displaystyle \tan \theta ^\circ = \frac{\text{opposite}}{\text{adjacent}}`

Let the horizontal distance be x. Substitute in known values:

`\displaystyle \tan 25^\circ = (150)/(x)`

Solve for x:

`\displaystyle x = (150)/(\tan 25^\circ)`

Use a calculator. Hence:

`x\approx 322\text{ feet}`

In conclusion, our answer is C.