Pythagoras and trigonometry basics

Pythagoras

In a right-angled triangle, $a^2 + b^2 = c^2$, where $c$ is the hypotenuse — the side opposite the right angle, always the longest.

To find the hypotenuse, add the squares. To find a shorter side, subtract: $b^2 = c^2 - a^2$. Choosing the wrong one is the single most common error.

The three ratios

$\sin\theta = \dfrac{\text{đối}}{\text{huyền}}$, $\cos\theta = \dfrac{\text{kề}}{\text{huyền}}$, $\tan\theta = \dfrac{\text{đối}}{\text{kề}}$. Label the sides relative to the angle you are using before choosing a ratio.

Which tool

Three sides and no angle: Pythagoras. An angle involved: trigonometry.