A particle of mass M is being suspended by two ropes from a horizontal ceiling. Rope A has a tension of 15N at 30 deg and rope B has a tension of xN at 45 deg, find M assuming the particle remains stationary.

This is a classic "picture frame" resolving forces question. By resolving horizontally we can use the "assuming the particle remains stationary" meaning the forces must cancel out, so, xCos45 = 15cos30 therefore x = 15/2*sqrt(6) (appox 18.4N). Using this information we can resolve vertically xSin45 + 15sin30 = Mg (it's important to notice here that we're using the weight as we're working in forces, it's also crucial that we use the value of g they give us in the question and we give our answer to the same amount of significant figures) by subsituting our value of x in and dividing by g, (9.8) we come to the answer of M = 2.1kg (it's also crucial to include units! they're easy marks to get, easy marks to miss!)