Question

A 60-yard long drawbridge has one end at ground level. The other end is initially at an incline of 5°.

How far off the ground is the raised end of the drawbridge in its initial setting?

Answer 1

5.229 yds

Explanation:

This is a classic right triangle trig problem. You have the length of the hypotenuse as the length of the drawbridge, you have the reference angle as the angle of inclination, and you are looking for the height of the triangle which will tell you how high off the ground the bridge is. From the reference angle's standpoint the height is the side opposite that angle. We also have the hypotenuse. The trig ratio we need will relate the reference angle, the hypotenuse and the side opposite the angle. This is the sin ratio:

`sin(\theta)=(opposite)/(hypotenuse)`

Fill in our info and solve for the side opposite:

`sin(5)=(x)/(60)` and

60 sin(5) = x

On your calculator in degree mode, find the value of x

60 sin(5) = 5.229 yds