sinθ=10/x How do I solve for x?
You can't - you have 2 unknowns and only one equation.
I suppose you could make x the subject
$$\\sin\theta =\frac{10}{x }\\\\ \frac{1}{sin\theta} =\frac{x}{10 }\\\\ \frac{10}{sin\theta} =x\\\\ x=\frac{10}{sin\theta}\\\\$$