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.

Explanation:

Step1: Recall tangent formula

We know that in a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, the height of the lighthouse (opposite side) is $h = 34$ meters and the distance from the boat to the base of the lighthouse (adjacent side) is $d=122$ meters. So, $\tan\theta=\frac{34}{122}$.

Step2: Calculate the tangent value

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

Step3: Find the angle

We use the inverse - tangent function, $\theta=\tan^{- 1}(0.2787)$. Using a calculator, $\theta\approx15.6^{\circ}$.

Step4: Round to the nearest degree

Rounding $15.6^{\circ}$ to the nearest degree gives $\theta\approx16^{\circ}$.

Answer:

$16$