Finding all sides of multiple triangles

[Guest]

I have a problem with one large right triangle divided, through the right angle, into one small and one medium triangle. The three corners of the large triangle are A, B, and C, and there is a line drawn from the right angle to point D on the large triangle's hypotenuse.

So the large triangle has sides AB, BC, CA.
The medium triangle has sides AB, BD, DA.
The small triangle has sides AD, DC, CA.

I am given the base - line AB - of the large triangle - 24 - and the longer part of the large triangle's hypotenuse- BD - 21. With line AD, these make up the medium size triangle, with the base of 21 and the hypotenuse of 24. I have no trouble using the Pythagorean theorum to find that DA is 11.61.

So the large triangle has sides 24, BC (which = 21 + DC), and CA
The Mdeium triangle has sides 24, 21, and 11.6
The small triangle has sides 11.6, DC, and CA

However, I still have to figure of the dimemsion of the little triangle.
How can I figure out the lengths of DC and CA?

 

[Gene]

The triangles are similar so
AB/BD=CA/DA
Pythagorean theorum does it from there.

 

[hbtcutie92]

theorum

a squared + b squared = c squared( c is always the hypotentuse)

 

[Denis]

Where does it say in the problem that AD is perpendicular to CB?
You're assuming that in your calculation of AD's length.