Answer:
B = 212 feet
Explanation:
Given that,
The angle of depression,
![\theta=27^(\circ)](https://img.qammunity.org/2022/formulas/mathematics/high-school/xs9zt9otgl694k8op1mp3eqngxe3lvxxei.png)
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)](https://img.qammunity.org/2022/formulas/mathematics/high-school/wn8yw58xd1xv9guy7wwn0czqp01krn7l08.png)
Where
B is the horizontal distance
![B=(h)/(\tan\theta)\\\\B=(108)/(\tan(27))\\\\B=211.96\ ft](https://img.qammunity.org/2022/formulas/mathematics/high-school/5rwkuwkzdvhu13destlrzhgnbienokwydo.png)
or
B = 212 feet
So, the horizontal distance from the boat to the base of the lighthouse is 212 feet.