Question

In a 30-60-90 triangle with the long leg being 12, what is the length of the hypotenuse?

a) 4√3
b) 3√8
c) 8√3
d) √2

Answer 1

The length of the hypotenuse in a 30-60-90 triangle with the long leg being 12 is √2.

Step-by-step explanation:

A 30-60-90 triangle has angles measuring 30 degrees, 60 degrees, and 90 degrees.

According to the Pythagorean theorem, in a 30-60-90 triangle, the hypotenuse is always two times the length of the shorter leg, and the longer leg is √3 times the length of the shorter leg.

In this case, the longer leg is given as 12. Therefore, the length of the hypotenuse is 2 * 12 = 24. So, the correct answer is option d) √2.