What is the value of sin 60°?

The value of sin 60° is derived from the properties of a 30-60-90 triangle, which is a special right triangle. In this triangle, the angles measure 30°, 60°, and 90°. The sides opposite these angles have a specific ratio: the side opposite the 30° angle is half the length of the hypotenuse, and the side opposite the 60° angle is √3/2 times the length of the hypotenuse.

To find sin 60°, we use the definition of sine, which is the ratio of the length of the side opposite the angle to the length of the hypotenuse. For the 60° angle in a 30-60-90 triangle, the opposite side to the 60° angle will be √3/2 and the hypotenuse is 1 (if we consider the hypotenuse to be of unit length).

Thus, sin 60° is calculated as follows:

sin 60° = (length of side opposite 60°) / (length of hypotenuse) = (√3/2) / 1 = √3/2.

The approximate decimal value of √3/2 is approximately 0.866