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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.

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 Near class=

Sagot :

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.

[tex]\sin \theta=\frac{opposite\text{ side}}{\text{hypotenuse}}[/tex]

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.

[tex]\sin 45=\frac{20ft}{x}[/tex]

Solve for x.

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

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

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