Question

Find x, the angle of depression from the top of a lighthouse that is 175 ft above water level to the waterline of a ship 914 ftoff shore. Round your answer to the nearest tenth of a degree.

Answer 1

Step 1

Use a trigonometric ratio to find x

$\begin{gathered} U\sin g\text{ TOA (Tangent, Opposite, Adjacent) written as} \\ \text{Tan}\theta=\frac{opposite}{\text{adjacent}} \end{gathered}$

where

$\begin{gathered} \theta=x^o \\ \text{opposite = 175ft} \\ \text{adjacent}=\text{ 914ft} \end{gathered}$

Step 2

Substitute and find x, the angle of depression from the top of a lighthouse

$\tan x^o=\frac{175}{914}$$\begin{gathered} x=\tan ^{-1}(\frac{175}{914})^{} \\ x=10.839^o \\ x\approx10.8^{\circ} \end{gathered}$

Hence, x, the angle of depression from the top of a lighthouse to the nearest tenth is 10.8°