Question

Find x, the angle of depression from the top of a lighthouse that is 157 ft above water level to the waterline of a ship 906 ftoff shore. Round your answer to the nearest tenth of a degree.

Answer 1

Answer:

9.8°

Explanation:

We can model the situation as follows:

So, we need to calculate the value of x.

The sides of the triangle and the angle x are related by the following trigonometric function:

$\begin{gathered} \tan x=\frac{Opposite\text{ side}}{Adjacent\text{ side}} \\ \tan x=\frac{157}{906} \end{gathered}$

Therefore, we can solve for x, using the inverse function of tangent as follows:

$\begin{gathered} \tan x=0.17 \\ x=\tan ^{-1}(0.17) \\ x=9.8 \end{gathered}$

Then, the angle of depression is 9.8°