SL 3.2—2d and 3d trig, sine rule, cosine rule, area

Before tackling non-right-angled triangles, we need a solid foundation in right-triangle trigonometry. Every right-angled triangle has three sides whose names depend on which angle $\theta$ you're working with:

• Hypotenuse — always the longest side, directly opposite the right angle.
• Opposite — the side that does not touch angle $\theta$.
• Adjacent — the non-hypotenuse side that does touch angle $\theta$.

The three primary trigonometric ratios relate these sides to the angle:

$\sin \theta =\frac{\text{opposite}}{\text{hypotenuse}},\cos \theta =\frac{\text{adjacent}}{\text{hypotenuse}},\tan \theta =\frac{\text{opposite}}{\text{adjacent}}$

There is also an important identity connecting tangent to sine and cosine. Dividing the numerator and denominator of $\frac{\text{opposite}}{\text{adjacent}}$ by the hypotenuse gives:

$\tan \theta =\frac{\sin \theta }{\cos \theta }$

This identity appears frequently in later trigonometry topics, so it's worth memorising now.