Question

value: 2
coconut palm trees can reach heights of up to 100 feet. suppose you are lying on the beach at a distance of 60 feet from a 48 - ft tall palm tree. what is the angle of elevation from your position to the top of the tree? round to the nearest tenth if necessary

a. 128.7°
b. 53.1°
c. 36.9°
d. 38.7°

Explanation:

Step1: Recall tangent formula

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, the height of the tree (opposite side) is 48 ft and the distance from the tree (adjacent side) is 60 ft. So, $\tan\theta=\frac{48}{60}$.

Step2: Simplify the tangent value

$\frac{48}{60} = 0.8$.

Step3: Find the angle

We know that $\theta=\arctan(0.8)$. Using a calculator, $\theta\approx38.7^{\circ}$.

Answer:

d. $38.7^{\circ}$