Answer
Shortest side = $\frac{4\sqrt 3 }{3} \approx 2.3$
Longest Side = $\frac{8\sqrt 3 }{3} \approx 4.6$
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° = 4
Therefore
Shortest side = $\frac{Side opposite 60°}{\sqrt 3}$ = $\frac{4}{\sqrt 3}$
Shortest side = $\frac{4\times\sqrt 3}{ \sqrt 3\times\sqrt 3}$ = $\frac{4\sqrt 3 }{3} \approx 2.3$
Longest Side = 2 $\times $ shortest side = 2$\times\frac{4\sqrt 3}{3}$
Longest Side = $\frac{8\sqrt 3 }{3} \approx 4.6$
