Chapter 12, Problem 3PST

To determine

To calculate : The height of the lighthouse.

Answer to Problem 3PST

The height of the lighthouse would be $138feet$

Explanation of Solution

Given information : The boat is $310feet$ away from the base of the lighthouse. And the angle of depression from the top of the lighthouse is $24°$ .

Formula used : There will be a right-angled triangle, and the height can be calculated using $a=b\tan (\theta )$ , Where $b$ is the base, and $a$ is the opposite and $\theta$ is the angle of depression from the top of the lighthouse.

Calculation : Calculate the height.

  $\begin{array}{l}a=b\tan (\theta )\\ a=310\times \tan (24°)\\ a=310\times 0.445\\ a=137.95\\ a=138feet\end{array}$