In a 30-60-90 triangle, the sides are in a specific ratio based on the angles. The side lengths are in the ratio \(1 : \sqrt{3} : 2\). Here’s how it breaks down:
- The side opposite the 30-degree angle (the shortest side) is \( \frac{1}{2} \) of the hypotenuse.
- The side opposite the 60-degree angle is \( \frac{\sqrt{3}}{2} \) of the hypotenuse.
Given that the hypotenuse is 8 cm:
- Calculate the side opposite the 60-degree angle: \[ \text{Side opposite 60-degree angle} = \frac{\sqrt{3}}{2} \times \text{Hypotenuse} = \frac{\sqrt{3}}{2} \times 8 = 4\sqrt{3} \]
Now, if you want a numerical approximation: \[ 4\sqrt{3} \approx 4 \times 1.732 = 6.928 \text{ cm} \]
Thus, the side opposite the 60-degree angle is \( 4\sqrt{3} \) cm or approximately \( 6.93 \) cm.
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