SOLUTION: triangle ABC is a right isosceles tri. with rt.angle at C.CD||AB &BD=BA.Find the angle DBC.?

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Question 979470: triangle ABC is a right isosceles tri. with rt.angle at C.CD||AB &BD=BA.Find the angle DBC.?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!

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If AC=BC=x, then
AB=BD=sqrt%282%29x
BCD=45
Then use the law of sines,
sin%28BDC%29%2F%28sqrt%282%29x%29=sin%2845%29%2Fx
sin%28BDC%29=%28sqrt%282%29%2F2%29%2F%28sqrt%282%29%29
sin%28BDC%29=1%2F2
BDC=30
Then,
BDC%2BDCB%2BDBC=180
30%2B45%2BDBC=180
DBC=180-75
DBC=105