Question

From the top of a 224-ft lighthouse, the angle of depression to a ship in the ocean is 22°. How far is the ship from the base of the lighthouse? Give your answer to the nearest foot.

Answer 1

Answer:

x=554.41 m

Step-by-step explanation:

It is given that,

Height of the lighthouse, OA=224 ft

The angle of depression to a ship in the ocean is 22 degrees.

We need to find the distance between ship and the base of the lighthouse. The figure is attached. We can use trigonometry to find x.

$\tan22=\dfrac{OA}{AB}\\\\\tan22=\dfrac{224}{x}\\\\x=\dfrac{224}{\tan22}\\\\x=554.41\ m$

So, there is a distance of 554.41 m between the ship and the lighthouse.