Question

In a 30-60-90 triangle, the length of the hypotenuse is 24 inches. What is the length of the side that is opposite from the 30° angle in

inches?

Answer 1

12 in.

Explanation:

In a 30-60-90 triangle:

short leg = x

hyp = 2x

long leg =
`x√(3)`

If we know that the hypotenuse = 24, then that means that 2x=24

Now if we solve for by by dividing both sides of the equation by 2 (you get x = 12), you can plug them in for the triangle ratios.

short leg = (12)

hyp = 2(12) = 24

long leg = (12)
`√(3)`

The 30° is adjacent to the long leg, so its opposite side would be the short leg. The short leg is 12 in., so the length of the side that is opposite from the 30° angle in inches is 12 inches.