Question

a playground slide is 14.5 feet long with an 8.5 - foot tall ladder.
what is the measure of the angle that the slide with the ground, x, to the nearest degree?
28°
36°
54°
62°

Explanation:

Step1: Recall the sine function

In a right - triangle, \(\sin x=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, the opposite side to the angle \(x\) is the height of the ladder (\(8.5\) ft) and the hypotenuse is the length of the slide (\(14.5\) ft). So, \(\sin x=\frac{8.5}{14.5}\).

Step2: Calculate \(\sin x\)

\(\sin x=\frac{8.5}{14.5}\approx0.5862\).

Step3: Find the angle \(x\)

Using the inverse - sine function \(x = \sin^{-1}(0.5862)\).
Using a calculator, \(x\approx36^{\circ}\).

Answer:

\(36^{\circ}\) (the second option)