Question

find x, the angle of depression from the top of a lighthouse that is 176 ft above water level to the waterline of a ship 832 ft off shore. round your answer to the nearest tenth of a degree.

x = ∘

Explanation:

Step1: Use the tangent function

The angle of depression \(x\) is equal to the angle of elevation from the ship to the top of the lighthouse. In a right - triangle, \(\tan x=\frac{\text{opposite}}{\text{adjacent}}\). Here, the opposite side is \(176\) and the adjacent side is \(832\). So, \(\tan x = \frac{176}{832}\).

Step2: Calculate the value of \(x\)

First, simplify \(\frac{176}{832}=\frac{11}{52}\approx0.2115\). Then, use the inverse tangent function \(x = \tan^{- 1}(0.2115)\). Using a calculator, \(x\approx11.9^{\circ}\).

Answer:

\(11.9\)