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: Identify the trigonometric relationship

We know that in a right - triangle (the skateboard ramp forms a right - triangle with the ground), the sine function is defined as $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, the angle of elevation $\theta = 20^{\circ}$, the hypotenuse (the length of the fiberboard) is $h = 19$ inches, and the height (opposite side) is $y$ (what we want to find). So, $\sin(20^{\circ})=\frac{y}{19}$.

Step2: Solve for \(y\)

We can rewrite the equation from Step1 as $y = 19\times\sin(20^{\circ})$.
We know that $\sin(20^{\circ})\approx0.3420$. Then $y=19\times0.3420$.
$y = 6.498$.

Answer:

$6.5$ inches