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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