Question

marques wants to use a sheet of fiberboard 36 inches long to create a skateboard ramp with a 30° 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 and the height), the sine of an angle of elevation \(\theta\) is given by \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 30^{\circ}\), the hypotenuse \(h = 36\) inches, and the opposite side \(y\) is the height of the ramp.

Step2: Apply the sine formula

Using the formula \(\sin\theta=\frac{y}{h}\), substituting \(\theta = 30^{\circ}\) and \(h = 36\) inches. Since \(\sin30^{\circ}=\frac{1}{2}\), we have \(\frac{1}{2}=\frac{y}{36}\).

Step3: Solve for \(y\)

Cross - multiply the equation \(\frac{1}{2}=\frac{y}{36}\) to get \(y=\frac{1\times36}{2}\).

Answer:

\(y = 18.0\) inches