\(\begin{aligned} a^2&=b^2+c^2-2bc \cos A \\\\ b^2&=a^2+c^2-2ac \cos B \\\\ c^2&=a^2+b^2-2ab \cos C \end{aligned}\)
| |
|
Example:
|
| |
|
In the diagram, \(ABC\) is a scalene triangle.
Find the length of \(AC\).
|
| |
\(\begin{aligned} AC^2&=AB^2+BC^2\\&\quad-2(AB)(BC) \cos 40^\circ \\\\ &=25^2+23^2\\&\quad-2(25)(23) \cos 40^\circ \\\\ &=273.05 \\\\ AC&=16.52 \text{ cm}. \end{aligned}\)
| |
| |
| \(\blacksquare\) Cosine rule can be used to find the unknown angles or sides of a triangle when |
| |
- Two sides and an included angle are known
- Three sides are known
|
| |
|
\(\blacksquare\) Included angle is the angle between two sides.
\(\angle C\) is the included angle between sides \(a\) and \(b\).
|
| |
