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.

Algebra.Com
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(39799)   (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(10810)   (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 =  

RELATED QUESTIONS


I really appreciate the help i'm getting from this website! Question: A rectangle has... (answered by rfer,solver91311)

If a+b=3 and a^3+b^3=6, given the formula (a+b)^3 = a^3+3a^2b+3ab^2+b^3, find the value... (answered by htmentor)

I need help trying to solve this problem. Thank you in advance, for helping me out. I... (answered by josgarithmetic,lpcruz)

The perimeter of a triangle is 85 inches.  The sides are: 2x, 2x+5, and X squared + 3... (answered by jim_thompson5910)

I need help trying to solve this problem. Thank you in advance, for helping me out. I... (answered by josgarithmetic)

I need help trying to solve this problem. Thank you in advance, for helping me out. I... (answered by Fombitz)

I need help trying to solve this problem. Thank you in advance, for helping me out. I... (answered by ewatrrr)

I need help trying to solve this problem. Thank you in advance, for helping me out. I... (answered by josgarithmetic)

I need help trying to solve this problem. Thank you in advance, for helping me out. I... (answered by josgarithmetic,lpcruz)