Volume of a cuboid with the Diagonal

Question

In the image, $PR=10$, $\angle APR=30º$ ($\overline {AP}$ face diagonal and $\overline {PR}$ Space diagonal) and $\angle PRQ=45º$ ($\overline {PR}$ space diagonal and $\overline {RQ}$ face diagonal)

Find the volume of the cuboid.

I need some help with this problem, first time facing a problem like this and i don't know how to proceed.

Answer 1

In the figure PQR is a right angled triangle and as one of the angles is 45 degrees we can conclude it is a issosellas triangle so PQ=10sin45
Triangle PAR is also a right angled triangle from that triangle we can conclude PA =10cos30 and AR = 10sin30
From PQA triangle we can find QA as we know PQ and PA
As we know all the 3 dimentions now we can find the volume