Question

In a triangle ABC if $\cos \, A + \cos \, B + \cos \, C = \frac{3}{2}$ , then the triangle is

• A. Right angled
• B. Right angled isoceles
• C. Equilateral
• D. None of these

Answer 1

Answer: (C)

Equilateral

Answer 2

We have, in $\Delta ABC$ $\cos\,A +\cos\,B + \cos\,C= \frac{3}{2}$ We know in $\Delta ABC$, $cos\, A + \cos\, B +\cos\,C \le \frac{3}{2}$ Since, $\cos\, A + \cos\, B +\cos\,C=\frac{3}{2}$ $\therefore A= B = C= 60^{\circ}$ Hence, $\Delta ABC$ is an equilateral triangle.