Solving a 30º-60º-90º Triangle

A right triangle has a hypotenuse that is twice the length of one leg. If this leg has a length of 15, what is the length of the remaining leg?

Incorrect. [[snippet]] This response is meant to distract you by making you think of the 8-15-17 recycled right triangle, but in a 8-15-17 right triangle, the length of the hypotenuse, 17, is not twice the length of the leg with a length of 15..

Incorrect. [[snippet]] If the two legs of the right triangle were both 15, then it would be a 45-45-90 recycled right triangle. The hypotenuse in this type of triangle is not twice the length of one leg, so this cannot be the answer.

Incorrect. [[snippet]] This response is meant to distract you by making you think of the 8-15-17 recycled right triangle. Further, the hypotenuse of a 8-15-17 right triangle has the length of 17, not one of the legs.

Correct. Only the 30-60-90 triangle has sides that follow the following ratios: $$\displaystyle a$$:$$a\sqrt{3}$$:$$2a$$ If the short leg is 15 (_a_ = 15), and the hypotenuse is twice this length (2_a_ = 30), then the longer leg should be $$\displaystyle a\sqrt{3}=15\sqrt{3}$$.

Incorrect. [[snippet]] The square root of 2 shows up in the 45-45-90 recycled right triangle, not the 30-60-90 recycled right triangle.

$$8$$

$$15$$

$$17$$

$$15\sqrt{2}$$

$$15\sqrt{3}$$