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

Answer:

B = 212 feet

Step-by-step 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 :

$\tan\theta=\dfrac{h}{B}$

Where

B is the horizontal distance

$B=\dfrac{h}{\tan\theta}\\\\B=\dfrac{108}{\tan(27)}\\\\B=211.96\ ft$

or

B = 212 feet

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