Question

faith wants to use a sheet of fiberboard 24 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: Identify the trigonometric ratio

We have a right triangle where the hypotenuse is 24 inches (the length of the fiberboard), the angle of elevation is \(26^\circ\), and we need to find the opposite side (the height \(x\)) to the angle. The sine function relates the opposite side and the hypotenuse: \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\).

Step2: Substitute the values

Substitute \(\theta = 26^\circ\), hypotenuse \(= 24\), and opposite \(= x\) into the sine formula: \(\sin(26^\circ)=\frac{x}{24}\).

Step3: Solve for \(x\)

Multiply both sides by 24: \(x = 24\times\sin(26^\circ)\). Calculate \(\sin(26^\circ)\approx0.4384\), then \(x\approx24\times0.4384 = 10.5216\). Round to the nearest tenth: \(x\approx10.5\).

Answer:

The ramp will rise approximately \(10.5\) inches from the ground at its highest end.