Question

a palm tree is 12.5 feet tall. the shadow is 18 feet long. find the angle of elevation.

if the angle of elevation is 34.78° use 1 in your code

if the angle of elevation is 43.98° use 2 in your code

if the angle of elevation is 56.02° use 5 in your code

Explanation:

Step1: Recall tangent formula

The tangent of the angle of elevation $\theta$ in a right - triangle (where the height of the tree is the opposite side and the length of the shadow is the adjacent side) is given by $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, the height of the tree (opposite side) $a = 12.5$ feet and the length of the shadow (adjacent side) $b = 18$ feet. So, $\tan\theta=\frac{12.5}{18}$.

Step2: Calculate the angle

We know that $\theta=\arctan(\frac{12.5}{18})$. Using a calculator, $\theta=\arctan(\frac{12.5}{18})\approx34.78^{\circ}$.

Answer:

1