Question

from a 200 ft observation tower on the beach, a man sights a whale in difficulty. the angle of depression of the whale is 7 degrees.how far is the whale from the shoreline

Answer 1

The whale is 24.54 feet away from the shoreline.

Step-by-step explanation:

Step 1:

The man is 200 feet from the ground and the angle at which he sees the whale is 7°.

So a right-angled triangle can be formed using these measurements. The angle of the triangle is 7° while the opposite side of the triangle measures x feet while the adjacent side of the triangle measures 200 feet.

We need to find the opposites side's length of the triangle.

Step 2:

Since we have the length of the adjacent side and need to calculate the length of the opposite side we use the tan of the given angle.

The opposite side of the triangle = x feet.

$\tan \theta = \frac{opposite side}{adjacent side} , tan (7) = 0.1227,$

$tan(7)=\frac{x}{200}, x = 0.1227 (200) = 24.54 feet.$

So the whale is 24.54 feet away from the shoreline.