How to solve $-20=15 \sin \theta- 30.98 \cos \theta$? How can I solve the following equation? $$-20=15 \sin \theta- 30.98 \cos \theta$$
I can't think of any way to solve it.  You can't factor out cosine because of the annoying little negative twenty, and if you divide by cosine you also get nowhere.

If you're familiar with basic vectors, you may reason the $a\cos\theta + b\sin\theta $  formula like this
$$20 = 30.98 \cos \theta - 15\sin \theta =  \langle 30.98, -15 \rangle \bullet \langle \cos \theta, \sin\theta \rangle = C \cos(\theta - \alpha) $$
$C = \sqrt{30.98^2 + 15^2}$
$\alpha = \arctan\left(- \dfrac{30.98}{15}\right)$
