In a 30-60-90 triangle, the lengths of the sides are in the ratio \(1 : \sqrt{3} : 2\). Here, the hypotenuse is the longest side, which corresponds to the "2" in the ratio.
Given that the hypotenuse is 8 cm, you can find the side opposite the 60-degree angle using the ratio. This side corresponds to \(\sqrt{3}\) in the ratio.
To find the lengths of the sides:
- The length of the side opposite the 30-degree angle (shortest side) is \( \frac{1}{2} \times \text{hypotenuse} = \frac{1}{2} \times 8 = 4 \) cm.
- The length of the side opposite the 60-degree angle is \( \frac{\sqrt{3}}{2} \times \text{hypotenuse} = \frac{\sqrt{3}}{2} \times 8 = 4\sqrt{3} \).
Thus, the side opposite the 60-degree angle is \( 4\sqrt{3} \) cm, which is approximately 6.93 cm.
The exact answer is: The side opposite the 60-degree angle is \( 4\sqrt{3} \) cm.
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