Find the exact value of \( \sin 60^{\circ} \)

The exact value of \( \sin 60^{\circ} \) is \( \frac{\sqrt{3}}{2} \). This angle is a key reference angle in trigonometry, commonly found in many geometric problems and calculations. By recognizing that a 60-degree angle forms an equilateral triangle divided in half, you can visualize how this value is derived from the sides of the triangle. If you think about a 30-60-90 triangle, the sides are in a specific ratio: the side opposite the 30° angle is half the hypotenuse, and the side opposite the 60° angle can be calculated using the Pythagorean theorem, giving you that wonderful \( \frac{\sqrt{3}}{2} \) for \( \sin 60^{\circ} \)!