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)
