In a 30-60-90 right triangle, the sides have a specific ratio:
- The side opposite the 30-degree angle is \( x \).
- The side opposite the 60-degree angle is \( x\sqrt{3} \).
- The hypotenuse is \( 2x \).
From the problem, we know that the side opposite the 60-degree angle is \( 73 - \sqrt{cm} \) long. According to the ratio, this side can be expressed as:
\[ x\sqrt{3} = 73 - \sqrt{cm} \]
To find \( x \), we can isolate \( x \):
\[ x = \frac{73 - \sqrt{cm}}{\sqrt{3}} \]
Next, the hypotenuse \( c \) of the triangle can be calculated as follows:
\[ c = 2x = 2 \left( \frac{73 - \sqrt{cm}}{\sqrt{3}} \right) = \frac{2(73 - \sqrt{cm})}{\sqrt{3}} \]
Thus, the length of the hypotenuse is:
\[ c = \frac{146 - 2\sqrt{cm}}{\sqrt{3}} \text{ cm} \]
So, that is the length of the hypotenuse in the triangle.
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