Trig - Law of sines and cosines - geometry problem

[LoyalKnight]

In the diagram below, triangle has been reflected over its median to produce triangle . If , , and , then find .



I tried several techniques, including assigning variables to sides and angles, and apply the law of sines and cosines, but to no avail. Does anybody know a way to solve for this?
Thanks.

 

[DrPhil]

In the diagram below, triangle has been reflected over its median to produce triangle . If , , and , then find .



I tried several techniques, including assigning variables to sides and angles, and apply the law of sines and cosines, but to no avail. Does anybody know a way to solve for this?
Thanks.

What have you tried? Can't tell where you are stuck if we don't see your work.

The picture as drawn shows BAB' as a straight line. Is anything said about that?

I assume you have accounted for the fact that M is the midpoint of BC (and also of B'C'). Lots of triangles that have the same area.

 

[LoyalKnight]

Nvm'd sir, I solved it. Basically I have to use a lot of symmetry and incorporate the law of cosines into there. Thanks!