Question

tamika wants to use a sheet of fiberboard 19 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 tenth of an inch if necessary.

Explanation:

Step1: Recall the sine function

The ramp forms a right - triangle, where the length of the fiberboard is the hypotenuse ($c = 19$ inches) and the height of the ramp is the side opposite the given angle ($\theta=20^{\circ}$). The sine function is defined as $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Let $h$ be the height of the ramp. So, $\sin(20^{\circ})=\frac{h}{19}$.

Step2: Solve for $h$

We can rewrite the equation from Step 1 as $h = 19\times\sin(20^{\circ})$.
We know that $\sin(20^{\circ})\approx0.3420$. Then $h = 19\times0.3420$.
$h=6.498$.

Answer:

$6.5$ inches