# 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.

$\therefore A=B=C=60^{\circ}$