Non-right-angled triangles — sine rule, cosine rule and area = ½ab·sin C

Even though both are on the formula sheet, students copy them down wrongly.

Algebra slips when solving $\tfrac12 ab\sin C$ for a side, or the cosine rule for an angle.

Using a non-included angle (not between $a$ and $b$) in $\tfrac12 ab\sin C$.

In the sine rule each side pairs with the angle opposite it: $\dfrac{a}{\sin A}$. Pairing a side with an adjacent angle instead of the opposite one gives the wrong equation.

For an angle use $\cos A=\dfrac{b^2+c^2-a^2}{2bc}$, with $a$ the side opposite $A$. Putting the wrong side as $a$, or losing the minus sign, gives a wrong angle.