Question

carlos designs the skateboard ramp shown in the diagram. enter the height of the ramp (h), in inches. round your answer to the nearest whole inch.

Explanation:

Step1: Use the sine function

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 22^{\circ}\), the hypotenuse is \(132\) inches, and the opposite side is \(h\). So, \(\sin(22^{\circ})=\frac{h}{132}\).

Step2: Solve for \(h\)

Multiply both sides of the equation \(\sin(22^{\circ})=\frac{h}{132}\) by \(132\). We get \(h = 132\times\sin(22^{\circ})\).
Since \(\sin(22^{\circ})\approx0.3746\), then \(h=132\times0.3746 = 49.4472\).

Answer:

\(49\)