# How do you solve for x in the given problem using right triangle trigonometry?

Apr 10, 2018

The length of $x$ is the length of the larger triangle minus the length of the smaller triangle.

#### Explanation:

For the larger triangle:
Let $L$ be the length of the side on the same side as $x$

$\tan \left(58\right) = \frac{140}{L}$

$L = \frac{140}{\tan} \left(58\right)$

For the smaller triangle:
Let $S$ be the length of the side on the same side as $x$

$\tan \left(20\right) = \frac{S}{140}$

$S = 140 \tan \left(20\right)$

$x = L - S$

$x = \frac{140}{\tan} \left(58\right) - 140 \tan \left(20\right)$