Question

Answer each of the following questions in one word or one sentence or as per exact requirement of the question.

If in a ∆ABC, $\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}$, then find the measures of angles A, B, C.

Answer 1

In ∆ABC,

$$\begin{gathered} \frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c} \\ \Rightarrow \frac{\cos A}{k\sin A}=\frac{\cos B}{k\sin B}=\frac{\cos C}{k\sin C}\left(\mathrm{Using}\mathrm{sine}\mathrm{rule}\right) \\ \Rightarrow \cot A=\cot B=\cot C \\ \Rightarrow A=B=C \end{gathered}$$

⇒ ∆ABC is an equilateral triangle.

∴ A = B = C = 60º