Trigonometry: SOH CAH TOA

The Ratios

$\sin\theta = \frac{\text{Opposite}}{\text{Hypotenuse}} \quad \cos\theta = \frac{\text{Adjacent}}{\text{Hypotenuse}} \quad \tan\theta = \frac{\text{Opposite}}{\text{Adjacent}}$

Labelling the Triangle

• Hypotenuse: longest side, opposite the right angle.
• Opposite: the side opposite the angle you're using.
• Adjacent: the side next to the angle (not the hypotenuse).

Finding a Side

1. Label O, A, H.
2. Choose the ratio (which two sides are involved?).
3. Substitute and solve.

Finding an Angle

Use the inverse function: $\theta = \sin^{-1}$, $\cos^{-1}$, or $\tan^{-1}$.