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 hypotenuse is the length of the slide (14.5 ft) and the opposite side to angle \( x \) is the height of the ladder (8.5 ft). 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, \( \sin^{-1}(0.5862)\approx36^\circ \) (rounded to the nearest degree).

Answer:

36° (corresponding to the option: 36°)