SOLUTION: The measure of the altitude of an equilateral triangle whose side has length 6 is?

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Question 530674: The measure of the altitude of an equilateral triangle whose side has length 6 is?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
This equilateral triangle has three equal sides of 6 units each.
To find the length of the height, drop a perpendicular line from any vertex to the opposite side, bisecting this side.
You now have two congruent right triangles in which the base is 3 and the hypotenuse is 6.
The height you are looking for is the third side of these right triangles.
Use the Pythagorean theorem to find this third side.
c%5E2+=+a%5E2%2Bb%5E2 c = 6, a = 3, and b = the height.
6%5E2+=+3%5E2%2Bb%5E2 Simplify.
36+=+9%2Bb%5E2 Subtract 9 from both sides.
27+=+b%5E2 Take the square root of both sides.
sqrt%2827%29+=+b Use only the positive solution.
b+=+3sqrt%283%29 This is the exact answer.
b+=5.2 This is the approximate answer.