# Math Help - Finding the height with trig

1. ## Finding the height with trig

Hi, can someone help me how to do this problem. Thanks a lot.

Assume that you are constructing a 20 ft road at 2 % gradient. PLease calculate the height of the road?

Thanks again for your help!!

2. This is a right triangle problem.

Treat the 20 ft. of road as your hypotenuse.

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

The opposite side is your height, so:

$\begin{array}{l}
\sin \theta = \frac{{height}}{{road}} \Rightarrow height = road \times \sin \theta \\
\\
height = 20ft. \times \sin 2^\circ = 0.7ft. \\
\end{array}$