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 makes with the ground, x, to the nearest degree?
28°
36°
54°
62°

Explanation:

Step1: Identify trigonometric ratio

We have a right triangle where the slide is the hypotenuse (\(14.5\) ft) and the ladder is the opposite side (\(8.5\) ft) to angle \(x\). So we use the sine function: \(\sin(x)=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{8.5}{14.5}\)

Step2: Calculate the angle

First, compute \(\frac{8.5}{14.5}\approx0.5862\). Then, take the inverse sine: \(x = \sin^{-1}(0.5862)\). Using a calculator, \(x\approx36^\circ\) (to the nearest degree).

Answer:

B. \(36^\circ\)