In triangle ABC, AB = 10, AC = 12, and BC = 8. Point M is on side BC such that angle BAM = angle CAM. Find BM.

Thank you!

BM = 4*sqrt(3).

1/ Use the law of cosines to find an angle B.

2/ Using the same method, find an angle A. Divide the value of this angle by 2.

3/ Now you have a triangle ABM with one known side and all 3 known angles.

4/ Using the law of sines, you can calculate the length of BM.