In a triangle ABC, D is the midpoint of BC. Join AD. Angle ADB = 45 degree and angle ACB = 30 degree. Find angle ABC.

(In reply to An algebraic solution by Eric)

I don't see how it is possible to let AD = DB = 1.  According to the problem statement, D is the midpoint of BC, so it is CD that equals DB.  What one needs to prove is that AB=BD×sqrt(2).  This can be done by calling B the origin, writing equations for the lines AC and AD, and solving for the coordinates of A.  This does work out and proves that ABC is similar to BDA so that angle ABC is 105 degrees just as I predicted in my earlier comment.

Posted by Richard on 2006-02-26 04:56:02