Finding exact values for trig functions of acute angles.
I have $\sin \theta = 3/5$.
I know that $y = 3$ and $r = 5$.
How the heck do I get $x$ if I don't know the angle?
If you know that $y=3$ and $r=5$, then because (presumably) the triangle is a right triangle with legs of length $x$ and $y$, and hypotenuse $r$, by the Pythagorean theorem we have that $$x^2+y^2=r^2,$$ hence $$x^2+9=25.$$ Thus $x^2=16$, and therefore $x=4$.