The fraction for sin 60 is √3 / 2.
This value is derived from the unit circle and the special right triangle with angles of 30-60-90. In this triangle, the side opposite the 60-degree angle is √3 times the length of the shorter leg, and the hypotenuse is twice the length of the shorter leg.
The sine function is defined as the ratio of the opposite side to the hypotenuse. Therefore, sin 60 = (√3 shorter leg) / (2 shorter leg) = √3 / 2.
