Question

katherine wants to use a sheet of fiberboard 18 inches long to create a skateboard ramp with a 17° 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 (where the ramp is the hypotenuse), if the hypotenuse \(c = 18\) inches and the angle of elevation \(\theta=17^{\circ}\), and we want to find the height \(h\) (opposite side to the angle \(\theta\)). The sine function is given by \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). So, \(\sin\theta=\frac{h}{c}\).

Step2: Substitute the values

Substitute \(c = 18\) and \(\theta = 17^{\circ}\) into the formula \(h = c\times\sin\theta\). We know that \(\sin(17^{\circ})\approx0.292\) (using a calculator, \(\sin(17^{\circ})=\sin(17\times\frac{\pi}{180})\approx0.292\)). Then \(h=18\times\sin(17^{\circ})\).

Step3: Calculate the value of \(h\)

\(h = 18\times0.292=5.256\)

Answer:

\(5.3\) inches