How do you solve this problem?

[dearlybelovedx3]

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http://i9.tinypic.com/6jof6sh.jpg

There is not enough variables to use SohCahToa or the pyhtagorean theorem. I am aware the three triangles are similar but I don
t know what to do. Urgent answers or help is needed.

 

[wjm11]

Set up ratios based on similar triangles:

DC/BD = BD/AD

You also know that AD + DC = 20 and that BD = 6.
Cross-multiply the ratio equation, do a couple of substitutions, and solve the quadratic.