SOLUTION: Thank you all beforehand for helping me out. I really appreciate your time and effort. Find the area of triangle ABC if AB = BC = 12 and angle ABC = 120.

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Question 1039827: Thank you all beforehand for helping me out. I really appreciate your time and effort.
Find the area of triangle ABC if AB = BC = 12 and angle ABC = 120.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39621) (Show Source):
You can put this solution on YOUR website!
Cut into two right triangles from point B to midpoint of AC.

Look at either of these right triangles. BC is opposite a 90 degree angle, a base leg is opposite a 60 degree angle, and altitude of the isosceles is opposite the 30 degree angle. SPECIAL RIGHT TRIANGLE.

Let 6 be the short leg of the special 30-60-90 right triangle.
12 is the length of the hypotenuse.
Let y be altitude or the other leg.

Put attention onto the original isosceles triangle.
You want the area.
, one-half of base times height;

Answer by MathTherapy(10555) (Show Source):
You can put this solution on YOUR website!
Thank you all beforehand for helping me out. I really appreciate your time and effort.
Find the area of triangle ABC if AB = BC = 12 and angle ABC = 120.

You can use: Area of triangle =
OR
The altitude that's drawn from ∠ABC to the base (AC) is the SHORTER side of one of the two 30-60-90 special right-triangles that're formed, since it's opposite the smaller of the
2 acute angles (). With the hypotenuse being 12, the shorter leg/height = , and the longer leg = . This means that the base = .
Therefore, area =