A trig ratio with numbers in it is really an equation with one blank. Take $\sin 30^\circ = \dfrac{o}{h}$: if you know the hypotenuse, MULTIPLY — $o = h\sin\theta$. If the blank is the hypotenuse itself, DIVIDE — $h = \dfrac{o}{\sin\theta}$. Unknown on top: multiply. Unknown on the bottom: divide. That’s the entire trick — and it’s exactly where exams set their traps.

Your built-in answer check comes free: sine and cosine of any sharp angle are numbers UNDER 1, so multiplying by them shrinks and dividing by them grows. The hypotenuse must finish as the longest side, every single time — if your ladder comes out shorter than the wall it reaches, the rearrangement lied, no appeal. And check the corner of the calculator screen says DEG. It matters today, and forever.