Answer
Shortest side = $2 \sqrt 3 \approx 3.46$
Longest Side = $4 \sqrt 3 \approx 6.93$
Work Step by Step
The longest side of a 30°–60°–90° triangle is twice the shortest side and the side opposite the 60° angle is $\sqrt 3$ times the shortest side.
Given that
Side opposite 60° = 6
Therefore
Shortest side = $\frac{Side opposite 60°}{\sqrt 3}$ = $\frac{6}{\sqrt 3}$
Shortest side = $\frac{2\times3}{\sqrt 3}$ = $\frac{2\times(\sqrt 3 \times\sqrt 3)}{\sqrt 3}$
Shortest side = $2\times \sqrt 3$ = $2 \sqrt 3 \approx 3.46$
Longest Side = 2 $\times $ shortest side = 2$\times2 \sqrt 3$ = $4 \sqrt 3$
Longest Side = $4 \sqrt 3 \approx 6.93$
