Question

Which set of values could be the side lengths of a 30-60-90 triangle?

A. {4,4/3,8/3}
B. {4,4/3,8}
C. {4,4/2,8}
D. {4,4/2,8/2}

Answer 1

In a 30-60-90 triangle there is a rule that shortest side of triangle (the one oposite from 30 degrees angle) is 2 times shorter than hypothenuse.
so lets search for that match in offered answers.

A. shortest side is 4√3 and hypothenuse is 8√3 which doesnt match condition.
B. 4 and 8 is just what we need. That is correct answer. but now we need to check third side. It has to be √3 times shortest side. it indeed matches
C. 4 and 8, atches first condition but other side isn't √3 times shortest
D. 4 and 8√2 doesnt match first condition