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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*}