Question

determining an angle of elevation
a boat is 122 meters from the base of a lighthouse that is 34 meters above sea level. what is the angle of elevation from the boat to the top of the lighthouse? round to the nearest degree.
34 m
122 m

Explanation:

Step1: Use the tangent function

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, the opposite side to the angle of elevation \(\theta\) is the height of the lighthouse (\(h = 34\) m) and the adjacent side is the distance from the boat to the base of the lighthouse (\(d=122\) m). So, \(\tan\theta=\frac{34}{122}\).

Step2: Calculate the value of \(\tan\theta\)

\(\tan\theta=\frac{34}{122}\approx0.2787\).

Step3: Find the angle \(\theta\)

We know that \(\theta=\arctan(0.2787)\). Using a calculator, \(\theta\approx15.6^{\circ}\).

Answer:

\(16^{\circ}\)