# Thread: Finding the length of a triangle

1. ## Finding the length of a triangle

Find RS.

Find TU.

Any help is appreciated! (:

2. Originally Posted by 4AM
Find RS.
Let x denote PR, then RQ = 50-x. Using the tangens function you can set up 2 equations:

$|\overline{RS}| = \dfrac{x}{\tan(32^\circ)}$ ..... and ..... $|\overline{RS}| = \dfrac{50-x}{\tan(26^\circ)}$

Set equal the RHS of the two equations and solve for x, afterwards you can use one of the two equations to get the length of RS. I've got $|\overline{RS}| \approx 44.94$

Find TU.
I've modified your sketch a little bit. (see attachment)

According to the drawing you can set up 2 equations:

$\tan(53.8^\circ)=\dfrac xy$ ..... and ..... $\tan(38.8^\circ)=\dfrac{x}{y+12.5}$

Solve the second equation for y, plug in this term into the first equation and solve for x.

I've got $|\overline{TU}| = x \approx 24.42$