Question

From the top of a 108-foot lighthouse, the angle of depression of a boat at sea is 27º. Find the horizontal distance from the boat to the base of the lighthouse, to the nearest tenth of a foot. (one decimal place).

Answer 1

B = 212 feet

Explanation:

Given that,

The angle of depression,
`\theta=27^(\circ)`

The height of the lighthouse, h = 108 feet

We need to find the horizontal distance from the boat to the base of the lighthouse. It can be calculated using trigonometry as follows :

`\tan\theta=(h)/(B)`

Where

B is the horizontal distance

`B=(h)/(\tan\theta)\\\\B=(108)/(\tan(27))\\\\B=211.96\ ft`

or

B = 212 feet

So, the horizontal distance from the boat to the base of the lighthouse is 212 feet.