If the side opposite a 60-degree angle in a 30-60-90 right triangle is 73–√ cm long, how long is the hypotenuse?
In a 30-60-90 right triangle, the side opposite the 60-degree angle is twice the length of the side opposite the 30-degree angle.
Let x be the length of the side opposite the 30-degree angle.
Therefore, the side opposite the 60-degree angle is 2x.
According to the problem, 2x = 73 - √ cm long.
Thus, x = (73 - √)/2 cm long.
The hypotenuse in a 30-60-90 right triangle is twice the length of the side opposite the 30-degree angle, which is 2(x) = 2((73 - √)/2) cm long.
Hence, the hypotenuse is (146 - 2√) cm long. Answer: \boxed{146 - 2\sqrt{\text{cm}}}.