# Find Length to Side of Triangle

• March 22nd 2011, 03:59 PM
kwikpwn
Find Length to Side of Triangle
http://i1103.photobucket.com/albums/...chia/natgh.jpg

This is how the problem started, and I need to find X. After working on it for awhile, all I could get to was this.

http://i1103.photobucket.com/albums/...ia/natgh-1.jpg

If you could please help me complete this, and tell me what you did, I'd deeply appreciate it. Thanks!
• March 22nd 2011, 04:22 PM
skeeter
(1) solve for $y$ using Pythagoras.

(2) similar triangles ...

$\dfrac{y}{52} = \dfrac{r}{48+r}$

solve for $r$.

(3) similar triangles again ...

$\dfrac{y}{48} = \dfrac{x}{48+2r}$

solve for x
• March 23rd 2011, 12:33 PM
bjhopper
Hi kwikpwn,
After you solve for y by the pythagorian theorem you can set up a simple equation in one unknown to find x.Use the property of tangents.

bjh