Question

The triangle formed by points $(0,0),(3,\frac{\pi }{2})$ and $(3,\frac{\pi }{6})$ is

• A. an isosceles triangle.
• B. a right angled triangle.
• C. an equilateral triangle.
• D. a right angled isosceles triangle.

Answer 1

The correct option is C an equilateral triangle.

Given points are $A(0,0)$, $B(3,\frac{\pi }{2})$ and $C(3,\frac{\pi }{6})$

$d=\sqrt{r_1^2+r_2^2-2r_1{r}_2\cos ({\theta }_1-{\theta }_2)}$
$AB=\sqrt{0+9-0}=3$
$BC=\sqrt{9+9-18\cos \frac{\pi }{3}}=3$
$AC=\sqrt{0+9-0}=3$
$\Rightarrow AB=BC=AC$
Hence, the triangle is equilateral