Question

natalie wants to use a sheet of fiberboard 30 inches long to create a skateboard ramp with a 28° 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 the trigonometric relationship

We know that the ramp forms a right - triangle, where the length of the fiberboard is the hypotenuse (\(c = 30\) inches) and the height of the ramp is the side opposite the angle of elevation (\(\theta=28^{\circ}\)). We use the sine function: \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\).

Step2: Substitute the values into the sine formula

Let \(h\) be the height of the ramp. Then \(\sin(28^{\circ})=\frac{h}{30}\).

Step3: Solve for \(h\)

Multiply both sides of the equation by \(30\): \(h = 30\times\sin(28^{\circ})\).
We know that \(\sin(28^{\circ})\approx0.4695\). So \(h=30\times0.4695 = 14.085\approx14.09\) inches.

Answer:

\(14.09\) inches