Question

bugs bunny was 33 meters below ground, digging his way toward pismo beach, when he realized he wanted to be above ground. he turned and dug through the dirt diagonally for 80 meters until he was above ground. what is the angle of elevation, in degrees, of bugs bunnys climb? round your final answer to the nearest tenth. angle of elevation = (see yellow hint below.)

Explanation:

Step1: Identify the trigonometric ratio

We know the opposite side ($33$ meters) and the hypotenuse ($80$ meters) of the right - triangle. We use the sine ratio. The sine of an angle $\theta$ in a right - triangle is given by $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$.
So, $\sin\theta=\frac{33}{80}$.

Step2: Calculate the angle

To find $\theta$, we take the inverse sine (arcsin) of $\frac{33}{80}$.
$\theta=\sin^{- 1}(\frac{33}{80})$.
Using a calculator, $\sin^{-1}(\frac{33}{80})\approx24.4^{\circ}$ (rounded to the nearest tenth).

Answer:

$24.4$