Question

The height of an equilateral triangle is side a is --------------------.

Answer 1

Answer:

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 to split the triangle into two equal 30-60-90 triangles

Now the side of the original equilateral triangle (let's call it "a")

is the hypotenuse of 30-60-90 triangle.Because 30-60-90 is a special triangle , we know that the sides are x , x root 3 , and 2x

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

Height of an equilateral triangle =

$\frac{ \sqrt{3a} }{2}$

Answer 2

Answer:

It should be memorized:

√3/a