1. **Problem:** Find the sine, cosine, and tangent of a 60-degree angle. 2. **Formulas:** - Sine of angle $\theta$: $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$ - Cosine of angle $\theta$: $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$ - Tangent of angle $\theta$: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$ 3. **Important rules:** - Angles are measured in degrees or radians; here, we use degrees. - For special angles like 60 degrees, values are well-known from the unit circle or special triangles. 4. **Intermediate work:** - For a 60-degree angle in an equilateral triangle split into two 30-60-90 right triangles: - Hypotenuse = 2 units - Opposite side (to 60°) = $\sqrt{3}$ units - Adjacent side (to 60°) = 1 unit 5. **Calculations:** - $\sin(60^\circ) = \frac{\sqrt{3}}{2}$ - $\cos(60^\circ) = \frac{1}{2}$ - $\tan(60^\circ) = \frac{\sqrt{3}}{1} = \sqrt{3}$ 6. **Explanation:** - The sine of 60 degrees is the ratio of the side opposite the angle to the hypotenuse. - The cosine is the ratio of the adjacent side to the hypotenuse. - The tangent is the ratio of the opposite side to the adjacent side. **Final answers:** $$\sin(60^\circ) = \frac{\sqrt{3}}{2}, \quad \cos(60^\circ) = \frac{1}{2}, \quad \tan(60^\circ) = \sqrt{3}$$