Right Triangles in Equilateral Triangle

Equilateral triangles do not have right angles, making them difficult to work with in regards to trigonometric equations. This can be solved by cutting the triangle in half, thus creating two triangles.



From the triangle above, we can find the length of the dotted line, 0, by pythagorean theorem.

This (1/2)² + O² = 1²

=

(1/4) + O² = 1

O = Sqrt(1-(1/4)) = sqrt(3/4) = sqrt(3)/2

The new angle at the top of the triangle can also be found, since all angles add up to 180, we get:

60 + y + 90 = 180
and so y=30 , exactly half of 60.

in degrees this is 30*(pi/180) = Pi/6