Question

If $\frac{cosA}{a}=\frac{cosB}{b}=\frac{cosC}{c}$ and the side $a=2$,

then area of triangle is equal to?

• A. $1$
• B. $\sqrt{3}$
• C. $\sqrt{5}$
• D. $\frac{\sqrt{3}}{2}$

Answer 1

The correct option is B $\sqrt{3}$

$\frac{cosA}{a}=\frac{cosB}{b}=\frac{cosC}{c}$

$\Rightarrow \frac{cosA}{2RsinA}=\frac{cosB}{2RsinB}=\frac{cosC}{2RsinC}$

$\Rightarrow tanA=tanB=tanC$

$A=B=C$

Now, since the triangle is an equilateral triangle. we have

Area $\to \frac{\sqrt{3}}{4}(side{)}^2=\sqrt{3}$