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
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