In a 30-60-90 triangle, the sides have a specific ratio: the side opposite the 30-degree angle is \(x\), the side opposite the 60-degree angle is \(x \sqrt{3}\), and the hypotenuse is \(2x\).
In your case, the side opposite the 60-degree angle is given as \(73 - \sqrt{cm}\). According to the relation in a 30-60-90 triangle, this length is equal to \(x \sqrt{3}\).
To find the hypotenuse, we first find \(x\):
\[ x \sqrt{3} = 73 - \sqrt{cm} \]
To find \(x\), we need to isolate it:
\[ x = \frac{73 - \sqrt{cm}}{\sqrt{3}} \]
Now, the hypotenuse will be:
\[ \text{Hypotenuse} = 2x = 2 \left(\frac{73 - \sqrt{cm}}{\sqrt{3}}\right) = \frac{2(73 - \sqrt{cm})}{\sqrt{3}} \]
However, without a specific numerical value for \(\sqrt{cm}\), we can't calculate a numerical value for the hypotenuse.
Assuming the question requires an approximate calculation for \(\sqrt{cm} = 0\) (just for simplicity), then:
\[ x = \frac{73}{\sqrt{3}} \approx 42.19 \]
Thus, the hypotenuse would be approximately:
\[ 2x \approx 84.39 \text{ cm} \]
None of the response options directly corresponds to this value.
If \(73 - \sqrt{cm} = 0\), then the side opposite 60-degree angle disappears and doesn’t actually make sense, but testing with the options given we look for integer results:
Notice that the best fitting option that might relate to typical results of a right triangle would best correspond to a mistaken setup here.
If I can guide back, could you clarify any additional requests?
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