To find the exact value of sin 60Β°, we can use the special right triangle with angles 30Β°-60Β°-90Β°.
In a 30Β°-60Β°-90Β° triangle, the side lengths are in the ratio 1 : \sqrt{3} : 2.
Therefore, in a triangle with a 60Β° angle, the side opposite the 60Β° angle is \sqrt{3} times the side opposite the 30Β° angle.
Since sin is opposite over hypotenuse, we have:
\sin 60Β° = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{\sqrt{3}}{2}
Therefore, the exact value of sin 60Β° is \boxed{\frac{\sqrt{3}}{2}}.