Area of Triangle

1. \(\,\)For any triangle \(ABC\),

• the side is denoted by a small letter.

• the angle is denoted by a capital letter.

\(\angle A=\angle BAC\)	Side \(a=\) Length \(BC\)
\(\angle B=\angle ABC\)	Side \(b=\) Length \(AC\)
\(\angle C=\angle CAB\)	Side \(c=\) Length \(AB\)

2. \(\,\)The formula for finding the area of triangle \(ABC\) is as followed:

\(\begin{align} & =\frac{1}{2}\times a\times b\times \sin C \\ & =\frac{1}{2}\times b\times c\times \sin A \\ & =\frac{1}{2}\times a\times c\times \sin B \\ \end{align}\)

3. \(\,\)The angle must be an included angle between two sides.

4. \(\,\)The formula work for triangles with external height.

Since \(\sin c=\sin 180{}^\circ -c\), hence, the formula for finding the area of triangle \(ABC\) works for both acute and obtuse included angle.