Question

rajani wants to use a sheet of fiberboard 31 inches long to create a skateboard ramp with a 19° 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.
10.1 in
9.8 in
29.3 in
10.7 in

Explanation:

Step1: Identify the trigonometric relationship

We have a right - triangle situation where the length of the hypotenuse (the fiberboard length) is $c = 31$ inches and the angle of elevation $\theta=19^{\circ}$, and we want to find the opposite side $h$ (height of the ramp). We use the sine function since $\sin\theta=\frac{opposite}{hypotenuse}$.
$\sin\theta=\frac{h}{c}$

Step2: Solve for the height $h$

Substitute $\theta = 19^{\circ}$ and $c = 31$ into the formula. We know that $\sin(19^{\circ})\approx0.3256$. Then $h = c\times\sin\theta$. So $h=31\times\sin(19^{\circ})$.
$h = 31\times0.3256=10.0936\approx10.1$ inches

Answer:

10.1 in