SOLUTION: The question I was given was: Suppose you have and equilateral triangle with a height of h feet. What is its area? I know I have to use the Pythagorean Theorem but I don't know ho

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Question 10255: The question I was given was: Suppose you have and equilateral triangle with a height of h feet. What is its area?
I know I have to use the Pythagorean Theorem but I don't know how to do this without knowing another side. Do you have any suggestions?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
I don't know about using the Pythagorean theorem on this problem if all you are given is the height of the equilateral triangle.
But you know (or should know) something else about the equilateral triangle...the interior angles are 60 degrees each.
And you know that the area of any triangle is: A = (1/2)bh so, if you can express the base, b, in terms of the height, h, and say, one of the known interior angles, then you have it.
I'm assuming that you are familiar with at least some elementary trigonometry.
The tangent of one of the base angles is h%2F%281%2F2%29b
or Tan%2860%29+=+h%2F%28%281%2F2%29b%29
or %281%2F2%29b+=+h%2FTan%2860%29 so the area of the equilateral triangle can written:
A+=+%28h%2FTan%2860%29%29h = h%5E2%2FTan%2860%29 = h%5E2%2F1.7321