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 sqrt(3) times the length of the side opposite the 30-degree angle.
Let x be the length of the side opposite the 30-degree angle.
Then x * sqrt(3) = 73 - sqrt(3).
So, x = (73 - sqrt(3)) / sqrt(3).
The hypotenuse is twice the length of the side opposite the 30-degree angle.
Therefore, the length of the hypotenuse is 2 * x = 2 * (73 - sqrt(3)) / sqrt(3) = (146 - 2 * sqrt(3)) / sqrt(3) = (146 sqrt(3) - 3) / 3 cm. Answer: \boxed{\frac{146 \sqrt{3} - 3}{3}} cm.