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how do you find the height of an equilateral triangle

 Jan 8, 2017
 #1
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An equalateral  has angles of 60 - 60 - 60

Drop a plumb line down from the vertex (hight point) that BISECTS the base.

Now you have TWO triangles of 60-30-90

You know the length of the shorter leg (it was a side BISECTED) and you know the HYPOTENUSE

Use pythag theorem to calculate the other LEG (which is the HEIGHT)

(you could also use law of sines etc)

 Jan 8, 2017
edited by ElectricPavlov  Jan 8, 2017
 #2
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You can also use this famous formula for the area of an equilateral triangle:

A =sqrt(3) / 4 x S^2, S=Side. Once you have the area, then just divide by S/2, since the area of ANY triangle is:Base x Height / 2.

 Jan 8, 2017

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