Question

1. a ramp is used to load suitcases on an airplane. if the cargo door is 7 feet from the ground and the angle formed by the end of the ramp and the ground is 25°, how long is the ramp? © gina wilson (all things algebra), 2014

Explanation:

Step1: Identify the trigonometric relationship

We have a right - triangle situation where the height of the cargo door from the ground (opposite side) is 7 feet and the angle between the ramp and the ground is 25°. We want to find the length of the ramp (hypotenuse). We use the sine function, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$.

Step2: Rearrange the formula to solve for the hypotenuse

If $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, then $\text{hypotenuse}=\frac{\text{opposite}}{\sin\theta}$. Here, $\theta = 25^{\circ}$ and the opposite side $a = 7$ feet. So, the length of the ramp $l=\frac{7}{\sin25^{\circ}}$.

Step3: Calculate the value

We know that $\sin25^{\circ}\approx0.4226$. Then $l=\frac{7}{0.4226}\approx16.6$ feet.

Answer:

The length of the ramp is approximately 16.6 feet.