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# Pythagoras’ Theorem and other Trigonometric Rules

### Area of any triangle

• The area of any triangle (when not given the perpendicular height) can be found by:
$\mbox{Area} = \frac{1}{2}b c \sin A$
• For example, find the area when $$b = 4$$, $$c=2$$ and $$A = 30^{\circ}$$:

\begin{eqnarray*}
\mbox{Area} &=& \frac{1}{2}b c \sin A \\
&=& \frac{1}{2} \times 4 \times 2 \times \sin 30^{\circ} \\
&=& 2
\end{eqnarray*}