Answer each of the following questions in one word or one sentence or as per exact requirement of the question.
Question:
Answer each of the following questions in one word or one sentence or as per exact requirement of the question.
If in a $\Delta \mathrm{ABC}, \frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}$, then find the measures of angles $A, B, C$.
Solution:
In ∆ABC,
$\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}$
$\Rightarrow \frac{\cos A}{k \sin A}=\frac{\cos B}{k \sin B}=\frac{\cos C}{k \sin C} \quad$ (Using sine rule)
$\Rightarrow \cot A=\cot B=\cot C$
$\Rightarrow A=B=C$
$\Rightarrow \triangle \mathrm{ABC}$ is an equilateral triangle.
$\therefore A=B=C=60^{\circ}$