Question

sydney wants to use a sheet of fiberboard 36 inches long to create a skateboard ramp with a 20° angle of elevation from the ground. how high will the ramp rise from the ground at its highest end? round your answer to the nearest hundredth of an inch if necessary.

Explanation:

Step1: Identify trigonometric ratio

The side $x$ is opposite the $20^\circ$ angle, and the hypotenuse is 36 inches. Use the sine function:
$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$

Step2: Substitute known values

Plug in $\theta=20^\circ$, hypotenuse=36:
$\sin(20^\circ) = \frac{x}{36}$

Step3: Solve for $x$

Rearrange to isolate $x$:
$x = 36 \times \sin(20^\circ)$

Step4: Calculate the value

Compute $\sin(20^\circ) \approx 0.3420$, then multiply:
$x \approx 36 \times 0.3420 = 12.312$

Step5: Round to nearest hundredth

Round the result to two decimal places:
$x \approx 12.31$

Answer:

12.31 inches