Question

How to prove formula of altitude of equilateral triangle?

Answer 1

Answer:

a√3 /2

Step-by-step explanation:

Equilateral triangles have sides of all equal length and angles of 60°. To find the height, we can draw an altitude to one of the sides in order to split the triangle into two equal 30-60-90 triangles.

Now, the side of the original equilateral triangle (lets call it "a") is the hypotenuse of the 30-60-90 triangle. Because the 30-60-90 triange is a special triangle, we know that the sides are x, x3–√, and 2x, respectively.

Thus, a = 2x and x = a/2.

Height of the equilateral triangle =a√3 /2

Answer 2

Answer:

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Your answer is attached in the attachment.

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