I need help with a geometry problem

I am trying to re-learn geometry and it isn't going so well. I remember the RULES but I don't know how to apply them. This one is giving me trouble:

http://i55.tinypic.com/nd09c6.gif

I have to use the Pythagorean theorem, correct? But how do I do that if I don't know the measure of TWO of the sides? I can find the measure of the smaller triangle but what does that do for me?

Thank you! Please explain. I need help :/

Please find the solution here!!

http://img816.imageshack.us/i/solutionx.jpg/

Thank you!!

Right triangles AEB and ACD are similar as
i) one angle A is common,
ii) ∠E = ∠C and
iii) ∠B = ∠D
=> AD/CD = AB/EB ... (1)

For right triangle AEB,
AB^2 = AE^2 + BE^2 = 8^2 + 6^2 = 100 cm^2
=> AB = 10 cm
Also, from the figure, CD = 15 cm and BE = 6 cm

Plugging in (1),
AD
= CD * (AB/EB)
= 15 * (10/6)
= 25 cm.

I *think*:

AEB and ACD are similar triangles- they have the same shape, and their sides are in the same proportion. BE corresponds to CD and AE corresponds to AC.

AE/AB = 4/3, so AC/CD = 4/3. CD = 15 cm, so AC = (4/3)*15 = 20cm

Then, as you say, use Pythagoras

AD^2 = AC^2 + CD^2 = 20^2 + 15^2 = 400 +225 = 625

AD = sqrt(625) = 25 cm <<<<

Here's how I would do the problem:
I would take the arctan of 6cm/8cm to gett ∠CAD
arctan( 6 / 8 ) = 36.9°
Now I would take the sin of that angle to find AD
sin( 36.9° ) = 15 / AD
AD = 25cm

from Pythagorean theorem, AB = 10
the two triangles are similar so
AD:AB = CD:BE
AD = AB*CD/BE = 25

I can see the problem we are facing. I think at least we must know the length of BC in order to get AD. I hope somebody will help us. Thank you

AD = SQRT [DC^2 + AC^2]
= SQRT[ 15^2 + {15*8/6}^2]
= SQRT[15^2 + 20^2]
= SQRT[ 25^2] as 5^2 [ 3^2 + 4^2 = 5^2]
= 25 cm