Trigonometry in right-angled triangles uses three ratios to connect sides and angles. Label the triangle relative to the angle you are working with — opposite (across from the angle), adjacent (next to it), and hypotenuse (longest side, opposite the right angle).
SOH CAH TOA: $$\sin\theta = \frac{\text{opposite}}{\text{hypotenuse}} \qquad \cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}} \qquad \tan\theta = \frac{\text{opposite}}{\text{adjacent}}$$
Finding a missing side: identify which ratio links the known angle, the known side, and the unknown side, then rearrange.
Example: In a right-angled triangle with hypotenuse $10\text{ cm}$ and angle $35°$, find the opposite side: $$\text{opposite} = 10 \times \sin 35° \approx 5.74\text{ cm}$$
Finding a missing angle: use the inverse function.
Example: opposite $= 6$, adjacent $= 8$: $$\theta = \tan^{-1}!\left(\frac{6}{8}\right) \approx 36.9°$$
Common error: labelling the triangle relative to the wrong angle, or dividing in the wrong direction when rearranging.