SOLUTION: In a given isosceles triangle, the base angles are 30 degrees. If the length of each leg is 20 cm, then what is the area of the triangle?

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Question 695710: In a given isosceles triangle, the base angles are 30 degrees. If the length of each leg is 20 cm, then what is the area of the triangle?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
We can calculate the lengths of legs in the right triangles.
h=20%2Asin%2830%5Eo%29=20%2A%281%2F2%29=highlight%2810%29cm
x=20%2Acos%2830%5Eo%29=20%2A%28sqrt%283%29%2F2%29=highlight%2810sqrt%283%29%29cm
The area of a triangle is calculated as
area=%281%2F2%29%2Abase%2Aheight
For the isosceles triangle, so
base=2x and height=h, so the area (in square centimeters) is
area=%281%2F2%29%2A%282x%29%2Ah=x%2Ah, so the area (in square centimeters) is
area=10%2A%2810sqrt%283%29%29=highlight%28100sqrt%283%29%29 = approx. 173.2 square cm