Final answer:
To find the hypotenuse of a 30-60-90 triangle from the longer leg, divide the length of the longer leg by √3 and then multiply by 2 to obtain the hypotenuse.
Step-by-step explanation:
To find the length of the hypotenuse of a 30-60-90 right triangle when given the length of the longer leg across from the 60-degree angle, you would multiply the length of the longer leg by two. This is because, in a 30-60-90 triangle, the ratio of the sides is 1:√3:2, meaning the hypotenuse is twice as long as the shorter leg, which is across from the 30-degree angle. However, when you're given the longer leg, across from the 60-degree angle, you know it's √3 times as long as the shorter leg. So, the hypotenuse is simply twice the length of the shorter leg, which we find by dividing the longer leg by √3 and then multiplying the resulting shorter leg by 2.
To recap, the operation is: (longer leg) / √3 x 2 = hypotenuse length.