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 have a right - triangle where the length of the hypotenuse (the fiberboard) is \(c = 30\) inches and the angle of elevation \(\theta=28^{\circ}\). We want to find the height \(h\) (opposite side to the angle \(\theta\)). Using the sine function: \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\).

Step2: Substitute the values into the formula

Substitute \(\theta = 28^{\circ}\) and \(c = 30\) into \(\sin\theta=\frac{h}{c}\). So \(h = c\times\sin\theta\). Since \(\sin(28^{\circ})\approx0.4695\), then \(h=30\times\sin(28^{\circ})\).

Step3: Calculate the value of \(h\)

\(h = 30\times0.4695=14.085\approx14.09\)

Answer:

\(14.09\) inches