The height of an equilateral triangle is 38". How long are the sides?

Question

 Hello! I am trying to hang some studio monitors (speakers), and everything I have read says to mount them as an equilateral triangle (left and right monitors spaced equally apart from each other on the wall and spaced an equal distance from the centre of the listeners head).

 The measurement from the bottom of the triangle to the tip (my head) is 38". What would the length of the sides equal to? 

 

Answer 1

If you draw the equilateral triangle... which is 60^o, 60^o, 60⁰

Then use the height.. in this case 38 inches to cut the equilateral

triangle into to equal right triangles of 30⁰, 60⁰, 90⁰

 

Label half the base as x

Label the full side (now the hypotenuse of a right triangle) as 2x

Label the height as 38

 

x² + h² = (2x)²  from Pythagorean Theorem

x² - 4x² = -h²

-3x² = -h²

x² = -h²/-3

x² = h²/3

x = √(h²/3)

x = h/√3

Side length = 2x = 2h/√3

 

Basically what I have done is worked out the formula for you.

This formula can be used for any height h to find the associated

side lengths for an equilateral triangle.

 

Side length = 2(38)/√3 = 76/√3 ≅ 43.88 inches