Question

find x, the angle of depression from the top of a lighthouse that is 170 ft above water level to the waterline of a ship 1153 ft off shore. round your answer to the nearest tenth of a degree.

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 the height of the lighthouse (\(170\) ft) and the adjacent side is the horizontal distance from the lighthouse to the ship (\(1153\) ft). So, \(\tan x=\frac{170}{1153}\).

Step2: Solve for \(x\)

Take the inverse tangent (arctan) of both sides: \(x = \arctan(\frac{170}{1153})\). Using a calculator, \(\frac{170}{1153}\approx0.1474\). Then \(x=\arctan(0.1474)\).

Answer:

\(x\approx8.4^{\circ}\)