Question

solving a real - world problem
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 the trigonometric ratio

We have a right - triangle where the opposite side to the angle $x$ is $8.5$ ft and the hypotenuse is $14.5$ ft. We use the sine ratio $\sin(x)=\frac{\text{opposite}}{\text{hypotenuse}}$.
So, $\sin(x)=\frac{8.5}{14.5}$.

Step2: Calculate the value of $\sin(x)$

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

Step3: Find the angle $x$

We know that $x = \sin^{- 1}(0.5862)$. Using a calculator, $x=\sin^{-1}(0.5862)\approx36^{\circ}$.

Answer:

$36^{\circ}$