Question

leah is standing at the bottom of the slide at the playground. waiting for leah is a vertical height of 9 feet, find the length of the slide. if the angle of elevation from the bottom of the slide to the top is 46°, and the slide leans

Explanation:

Step1: Identify the trigonometric relationship

We have a right - triangle situation where the vertical height (opposite side) of the slide is 9 feet and the angle of elevation is 46°. We use the sine function since $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$.

Step2: Set up the equation

Let the length of the slide (hypotenuse) be $l$. Given $\theta = 46^{\circ}$ and the opposite side $a = 9$ feet. So, $\sin46^{\circ}=\frac{9}{l}$.

Step3: Solve for $l$

We know that $l=\frac{9}{\sin46^{\circ}}$. Since $\sin46^{\circ}\approx0.7193$, then $l=\frac{9}{0.7193}\approx12.51$ feet.

Answer:

The length of the slide is approximately 12.51 feet.