Question

1. max built a skateboarding ramp that is 16 inches high. the angle formed by the ramp and the ground is 21°. what is the length of the ramp?

Explanation:

Step1: Identify the trigonometric relationship

We know the height (opposite side) of the right - triangle formed by the ramp, ground and height is \(h = 16\) inches and the angle \(\theta=21^{\circ}\). Let the length of the ramp be \(l\) (hypotenuse). Using the sine function \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), so \(\sin(21^{\circ})=\frac{16}{l}\).

Step2: Solve for \(l\)

Rearrange the formula \(l=\frac{16}{\sin(21^{\circ})}\).
We know that \(\sin(21^{\circ})\approx0.3584\). Then \(l=\frac{16}{0.3584}\approx44.64\) inches.

Answer:

The length of the ramp is approximately \(44.6\) inches.