# JEE Main & Advanced Mathematics Trigonometric Equations Relation Between Sides and Angles

## Relation Between Sides and Angles

Category : JEE Main & Advanced

A triangle has six components, three sides and three angles. The three angles of a $\Delta ABC$ are denoted by letters $A,\,\,B,\,\,C$ and the sides opposite to these angles by letters $a,\,\,b$ and $c$ respectively. Following are some well known relations for a triangle (say $\Delta ABC$)

• $A+B+C={{180}^{o}}$ (or $\pi$)
• $a+b>c,\,\,b+c>a,\,\,c+a>b$
• $|a-b|<c,|b-c|<a,|c-a|<b$

Generally, the relations involving the sides and angles of a triangle are cyclic in nature, e.g. to obtain the second similar relation to $a+b>c,$ we simply replace $a$ by $b,\,\,b$ by $c$ and $c$ by $a$. So, to write all the relations, follow the cycles given.

The law of sines or sine rule : The sides of a triangle are proportional to the sines of the angles opposite to them  i.e., $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}=k,\,(say)$

More generally, if $R$ be the radius of the circumcircle of the triangle $ABC,\,\,\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}=2R$.

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