Unit Circle Activity

The unit circle allows the triangle to be formed within the circle. The special right triangle 30,60, 90 is based on the 30 degree reference angle in the first quadrant. Since the unit circle radius equals one then the hypotenuse of the triangle will also be one. The opposite side of the triangle will be 1/2 because the hypotenuse is twice as long, and the opposite side is shorter. The adjacent side will the square root of three over 2 because it is square root of three from the opposite side divide by 1/2. 

The 60, 30, 90 is based on the 60 reference angle, and similar to the 30, 60, 90 triangle. The hypotenuse will be one and the adjacent side will be one half due to its shorter length, and the the other side will also be the square root of three similar to the 30, 60, 90 triangle.

The 45, 45, 90 triangle is based on the 45 degree reference angle. The hypotenuse will be the square root of 2 because the sides are congruent, but will be divided by another square root of two which will give us one ( the radius of the circle unit). The other two sides will be the square root 2 over 2 because they are congruent. These triangle are formed by the unit circle reference angles.