Here is the processed version.

Given \(30-60-90\) triangle,

Hypotenuse \(=\) \(q\sqrt3\)

The short side that is opposite of the \(30\) degree angle is \(p\sqrt2\)

And the long side that is opposite to the \(60\) degree angle is \(p\sqrt6\)

Find the values of \(p\) and \(q.\)

Anyways, \(2p\sqrt2 = q\sqrt3\), techincally, there is 1 equation and 2 variables, making this problem more difficult to solve.

I'm going to have this problem solved by someone else (Because unfortunately, I must do my homework).