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=(Perpendicular)/(Base)`

In triangle ABC,

`\tan C=(AB)/(BC)`

`\tan 18^\circ=(280)/(BC)`

`BC=(280)/(\tan 18^\circ)`

Using a calculator, we get

`BC=(280)/(0.3249)`

`BC=861.80363...`

`BC\approx 862`

Therefore, the boat is 862 feet away from shore.