Question

11.) a straight waterslide is 175 feet above ground and is 200 feet long. what is the angle of depression to the bottom of the slide?

Explanation:

Step1: Identify the trig - ratio

We have a right - triangle situation where the height (opposite side to the angle of depression) is $a = 175$ feet and the length of the waterslide (hypotenuse) is $c=200$ feet. We use the sine function $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$.
$\sin\theta=\frac{175}{200}$

Step2: Simplify the ratio

Simplify $\frac{175}{200}=\frac{7}{8}=0.875$.

Step3: Find the angle

We know that $\theta=\sin^{- 1}(0.875)$. Using a calculator, $\theta=\sin^{-1}(0.875)\approx61.04^{\circ}$.

Answer:

Approximately $61.04^{\circ}$