Question

The perimeter of the triangle formed by the points $(0,0)$, $(3,\frac{\pi }{3})$ and $(3,\frac{2\pi }{3})$ is:

• A. $3$
• B. $6$
• C. $9$
• D. $18$

Answer 1

Answer: (C)

$9$

Distance between two points is
$d=\sqrt{r_1^2+r_2^2-2r_1{r}_2\cos ({\theta }_1-{\theta }_2)}$
Given points are $A(0,0)$, $B(3,\frac{\pi }{3})$ and $C(3,\frac{2\pi }{3})$
$AB=\sqrt{0+9-0}=3$
$BC=\sqrt{9+9-18\cos (-\frac{\pi }{3})}=3$
$AC=\sqrt{0+9-0}=3$
Perimeter$=9$ units