document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #429062 by KMST(5328) $\"\"$ $\"About$

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We can calculate the lengths of legs in the right triangles.
\n" ); document.write( " $\"h=20%2Asin%2830%5Eo%29=20%2A%281%2F2%29=highlight%2810%29\"$ cm
\n" ); document.write( " $\"x=20%2Acos%2830%5Eo%29=20%2A%28sqrt%283%29%2F2%29=highlight%2810sqrt%283%29%29\"$ cm
\n" ); document.write( "The area of a triangle is calculated as
\n" ); document.write( " $\"area=%281%2F2%29%2Abase%2Aheight\"$
\n" ); document.write( "For the isosceles triangle, so
\n" ); document.write( " $\"base=2x\"$ and $\"height=h\"$ , so the area (in square centimeters) is
\n" ); document.write( " $\"area=%281%2F2%29%2A%282x%29%2Ah=x%2Ah\"$ , so the area (in square centimeters) is
\n" ); document.write( " $\"area=10%2A%2810sqrt%283%29%29=highlight%28100sqrt%283%29%29\"$ = approx. 173.2 square cm \n" ); document.write( "

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