Question

piper wants to use a sheet of fiberboard 33 inches long to create a skateboard ramp with a 26° 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: Use sine function

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 26^{\circ}\), the hypotenuse is \(33\) inches and the opposite side is \(x\) (the height we want to find). So, \(\sin(26^{\circ})=\frac{x}{33}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\sin(26^{\circ})=\frac{x}{33}\) by \(33\). We get \(x = 33\times\sin(26^{\circ})\).
Using a calculator, \(\sin(26^{\circ})\approx0.4384\). Then \(x=33\times0.4384 = 14.4672\approx14.5\).

Answer:

\(14.5\)