Given: ∆ABC is isosceles

Question

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

Answer 1

m∠CAB = m∠CBA = 30º

m∠BCM = 90º

BM = 24 ... 30-60-90 TRIANGLE

AM = CM

Answer 2

AB=36

Thanks

Answer 3

Can you please elaborate on the explanation?

Answer 4

Wait why is AM=CM? Thanks!

Answer 5

expaind

Answer 6

correct

Answer 7

idk how u got that answer
I entered it in on me online hw but it says its wrong

Answer 8

For me it is correct

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

thanks evan