Question

in the diagram below given that XY = 30cm, XZY =30° and YZ = x, is it possible to solve for x using the theoram of pythagoras​

Answer 1

No, you need to know another angle to prove that it is a right triangle to use the Pythagorean theorem.

If you did have an additional side length, that needed angle could be calculated and then use the Pythagorean to prove.