What are the rules of trianglenometrry

For right-angled triangles, the basic trigonometric ratios are used:

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

For any triangle (not just right-angled), the following rules apply:

The Sine Rule relates the ratio of a side length to the sine of its opposite angle:

$$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$

The Cosine Rule is used to find a side when two sides and the included angle are known, or to find an angle when all three sides are known:

$$a^2 = b^2 + c^2 - 2bc\cos A$$

The Area Rule allows you to calculate the area of a triangle using two sides and the included angle:

$$\text{Area} = \frac{1}{2}ab\sin C$$