Question

Given: ∆ABC is isosceles m∠ACB = 120° M ∈ AB , CM = 12 m∠BMC = 60° Find: AB

Answer 1

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)/(\sin 60)`
Solving for BC we get :
`BC=20.7`
We apply the law of sin again on the isosceles triangle ABC like this:

`(AB)/(\sin 120) = (20.7)/(\sin 30)`
Solving for AB we get:

`AB=36`