Question

A slide on a playground rises at a 45° angle. The top of the slide is 20 feet above the ground. How far does a child travel down the slide? Round answer to the nearest hundredth place.

Answer 1

x=Let's illustrate the problem first. Assuming the height of the slide is right-angled to the ground.

To determine the length of the slide, we can use sine function.

`\sin \theta=\frac{opposite\text{ side}}{\text{hypotenuse}}`

In the illustration, the opposite side of the angle 45° is 20ft whereas the hypotenuse is the length of the slide. Let's plug in these values to the function above. Assume x = length of the slide.

`\sin 45=(20ft)/(x)`

Solve for x.

`\begin{gathered} x=(20ft)/(\sin 45) \\ x=20\sqrt[]{2}ft \\ x\approx28.28ft \end{gathered}`

The length of the slide and the distance the child has to travel down the slide is approximately 28.28 ft. (Option C)