SOLUTION: Prove that the length of the altitude of equilateral triangle of side 'a' is square root of 3/2 *a square?

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Question 207293: Prove that the length of the altitude of equilateral triangle of side 'a' is square root of 3/2 *a square?
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Dropping the altitude, creates 2 right triangles. Each triangle has a hypotenuse of length a, a shorter side with length a/2 and the altitude h.
Using Pythagorean theorem
a%5E2+=+%28a%2F2%29%5E2+%2B+h%5E2
a%5E2+-+a%5E2%2F4+=+h%5E2
%283a%5E2%29%2F4+=+h%5E2
sqrt%283a%5E2%2F4%29+=+h
sqrt%283%29%2Aa%2F2+=+h