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?

Explanation:

Step1: Identify the trig - function

We have a right - triangle situation where the height (opposite side to the given angle) is 7 feet and the angle with the ground is 25°. We use the sine function since $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Let the length of the ramp be $x$ (hypotenuse). So, $\sin(25^{\circ})=\frac{7}{x}$.

Step2: Solve for $x$

Cross - multiply to get $x\sin(25^{\circ}) = 7$. Then $x=\frac{7}{\sin(25^{\circ})}$.
We know that $\sin(25^{\circ})\approx0.4226$. So, $x=\frac{7}{0.4226}\approx16.6$.

Answer:

The length of the ramp is approximately 16.6 feet.