Question

From the top of a lighthouse 280 feet tall, to keep her spot a ship in distress at an angle of depression of 18°. How far is the boat from shore(The base of the lighthouse) round to the nearest foot

Answer 1

Given:

Height of the lighthouse = 280 feet

The angle of depression from the top of the lighthouse to a ship = 18°.

To find:

The distance between boat and shore.

Solution:

Draw a diagram by using the given information.

In a right angle triangle,

$\tan \theta=\dfrac{Perpendicular}{Base}$

In triangle ABC,

$\tan C=\dfrac{AB}{BC}$

$\tan 18^\circ=\dfrac{280}{BC}$

$BC=\dfrac{280}{\tan 18^\circ}$

Using a calculator, we get

$BC=\dfrac{280}{0.3249}$

$BC=861.80363...$

$BC\approx 862$

Therefore, the boat is 862 feet away from shore.