What is sin 60

The following illustrates geno3141's answer.

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If you want to find the sin(60°) without using a calculator, draw a right triangle with angles of 60°, 30°, and 90°.

From geometny, it can be shown that the length of the side opposite the 60° angle is √3, the side adjacent to the 60° angle is 1, and the hypotenuse is 2 (or multiples of these numbers).

Sin is defined to be the length of the opposite side divided by the length of the hypotenuse:  sin  =  opp / hyp.

sin(60°)  =  √3 / 2