How do you calculate the height of an equilateral triangle?

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How do you calculate the height of an equilateral triangle?

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Answer 1 · 2015-11-26T10:31:39

The height of the equilateral triangle is #h=(asqrt(3))/2#

Explanation:

If you draw a height in an equilateral triangle you can see that the triangle is divided in 2 right angled triangles in which: sides #a# are hypothenuses, height is one cathetus (common for both triangles), the other is equal to #a/2#, so if we use the Pythagorean theorem we get:

#(a/2)^2+h^2=a^2#

#h^2=a^2-(a/2)^2#

#h^2=a^2-a^2/4#

#h^2=3/4a^2#

#h=(asqrt(3))/2#

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How do you calculate the height of an equilateral triangle?

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