Question

which set of values could be the side lengths of a 30 - 60 - 90 triangle?
a. {6, 12, 12\sqrt{2}}
b. {6, 6\sqrt{3}, 12}
c. {6, 6\sqrt{2}, 12}
d. {6, 12, 12\sqrt{3}}

Explanation:

Step1: Recall side - length ratio

In a 30 - 60 - 90 triangle, the side - length ratio is $1:\sqrt{3}:2$. That is, if the shortest side (opposite the 30 - degree angle) is $x$, the side opposite the 60 - degree angle is $x\sqrt{3}$, and the hypotenuse (opposite the 90 - degree angle) is $2x$.

Step2: Check each option

Let's assume $x = 6$. Then the side opposite the 30 - degree angle is $x=6$, the side opposite the 60 - degree angle is $x\sqrt{3}=6\sqrt{3}$, and the hypotenuse is $2x = 12$.

Answer:

B. $\{6,6\sqrt{3},12\}$