Question

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?

Answer 1

Answer: $16.56\ ft$

Step-by-step explanation:

You must draw a right triangle as the one attached, where "x" is the lenght  in feet of the ramp.

You need to use the following Trigonometric Identity:

$sin\alpha=\frac{opposite}{hypotenuse}$

In this case you can identify that:

$\alpha =25\°\\\\opposite=7\\\\hypotenuse=x$

Now you must substitute these values into $sin\alpha=\frac{opposite}{hypotenuse}$:

$sin(25\°)=\frac{7}{x}$

Finally, you must solve for "x" in order to find its value.

This is:

$sin(25\°)=\frac{7}{x}\\\\xsin(25\°)=7\\\\x=\frac{7}{sin(25\°)}\\\\x=16.56$