In a 30-60-90 triangle, the ratios of the lengths of the sides opposite the angles are as follows:
- The side opposite the 30-degree angle is \( x \).
- The side opposite the 60-degree angle is \( x\sqrt{3} \).
- The hypotenuse (opposite the 90-degree angle) is \( 2x \).
In your case, you mentioned that the side opposite the 60-degree angle is \( 7\sqrt{3} \) cm. According to the side ratios:
\[ x\sqrt{3} = 7\sqrt{3} \]
From this, we can deduce that:
\[ x = 7 \]
Now, we can find the length of the hypotenuse:
\[ \text{Hypotenuse} = 2x = 2(7) = 14 \text{ cm} \]
So, the hypotenuse is 14 cm.
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