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 ratio: \( \sin(x) = \frac{\text{opposite}}{\text{hypotenuse}} \)
\( \sin(x) = \frac{8.5}{14.5} \)

Step2: Calculate the angle

First, compute \( \frac{8.5}{14.5} \approx 0.5862 \). Then, take the inverse sine: \( x = \sin^{-1}(0.5862) \)
Using a calculator, \( x \approx 36^\circ \) (to the nearest degree)

Answer:

36° (corresponding to the option: 36°)