In a 30-60-90 triangle, the lengths of the sides are in a specific ratio:
- The side opposite the 30-degree angle (let's call it \( x \))
- The side opposite the 60-degree angle (which is \( \sqrt{3} \times x \))
- The hypotenuse (which is \( 2 \times x \))
You mentioned that the side opposite the 60-degree angle is \( 7\sqrt{3} \) cm long. According to the properties of 30-60-90 triangles, we can set up the relationship as follows:
\[ \text{Side opposite 60 degrees} = \sqrt{3} \times x \]
Substituting the given value:
\[ \sqrt{3} \times x = 7\sqrt{3} \]
To find \( x \), we divide both sides by \( \sqrt{3} \):
\[ x = 7 \]
Now, we can find the length of the hypotenuse using the relationship \( 2 \times x \):
\[ \text{Hypotenuse} = 2 \times x = 2 \times 7 = 14 \]
Therefore, the length of the hypotenuse is \( \boxed{14} \) cm.
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