Answer:
B = 212 feet
Step-by-step explanation:
Given that,
The angle of depression, [tex]\theta=27^{\circ}[/tex]
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 :
[tex]\tan\theta=\dfrac{h}{B}[/tex]
Where
B is the horizontal distance
[tex]B=\dfrac{h}{\tan\theta}\\\\B=\dfrac{108}{\tan(27)}\\\\B=211.96\ ft[/tex]
or
B = 212 feet
So, the horizontal distance from the boat to the base of the lighthouse is 212 feet.
