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

Isosceles and Equilateral Triangles

Isosceles triangles are triangles with two sides of equal length. Therefore if we know the measure of one angle we can calculate the measure of the remaining angles. If we know that the measure of the unequal angle is 30 degrees we can deduce that the remaining angles must each equal 75 degrees.

Let x equal the measure of our two equal angles. This 2x + 30 must equal 180, or the total measure of degrees in a triangle.

2x + 30 = 180
2x=150
x=75


Equilateral triangles are triangles which have sides of equal length and therefore angles of equal length. The angles of an equilateral triangle will always equal 60 degrees or (pi)/3 radians.