Given: ∆ABC is isosceles

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

M is on line segment AB

I saw that someone has already post this question, but I didn't find the answer so I reposted it to c if someone could put the answer

AB=36

Thanks

Can you please elaborate on the explanation?

Since the angle is isosceles, angle A and angle B have the same measure,

The sum of the angles of any triangle is 180°.
So 2 times the measure of angle B plus 120° = 180°, then the equation:
2x+120=180

Solving for x we get:
x=30
Now we use the law of sine on the triangle BMC like this:
12/sin30 = BC/sin60

Solving for BC we get :
BC=20.7
We apply the law of sin again on the isosceles triangle ABC like this:
AB/sin120=20.7/sin30

Solving for AB we get:

AB=36

There must be another way without law of sins cos or tan.

I hope there is another simpler way of explaining it...

expaind

For me it is correct

correct

thanks evan

Wait why is AM=CM? Thanks!