Find the shortest side if

Question

In the $\triangle PQR$ angle P= 60 degrees & angle Q= 90 degrees . Find the length of the shortest side.

Any Ideas on how to begin

Many Thanks :)

Answer 1

You have a 30-60-90 triangle, so if the length of the shortest side (opposite 30 degrees angle) is x, the side opposite the 60 degree angle is $\sqrt{3} x$ and and the hypotenuse (side opposite the 90 degree angle) is $2 x$.

You will need one of the side lengths (and know it is for the shortest/ longest leg or hypotenuse) in order to compute $x$ (which gives you the other two side lengths).

Pictorially (from here):