Question

bugs bunny was 42 meters below ground, digging his way toward albuquerque, when he realized he wanted to be above ground. he turned and dug through the dirt diagonally for 100 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.

image of a right triangle with hypotenuse 100 and vertical side 42
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right triangle word problems

Explanation:

Step1: Identify the triangle type

This is a right triangle problem, where the vertical side (opposite to the angle of elevation) is 42 meters, and the hypotenuse (the slant distance) is 100 meters. We use the sine function, as $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$.

Step2: Set up the sine formula

Let $\theta$ be the angle of elevation. Then $\sin(\theta)=\frac{42}{100}=0.42$.

Step3: Calculate the angle

To find $\theta$, we take the inverse sine (arcsin) of 0.42: $\theta=\arcsin(0.42)$. Using a calculator, $\arcsin(0.42)\approx24.83^\circ$. Rounding to the nearest tenth gives $24.8^\circ$.

Answer:

$24.8$