Given: ∆ABC is isosceles

m∠ACB = 120°
m∠BMC = 60°
CM = 12
Find: AB

M is on line segment AB

1 answer

surely by now you could have figured this out.

Since ∆ABC is isosceles, ∠A = ∠B = 30°

Therefore, ∆BMC is a 30-60-90 right triangle, with ∠MCB = 90°

So, BC = 12√3

Now drop an altitude from C to AB and use BC to find AB.