Question

The angle of a triangle are in the ratio of $1:2:3$. The greatest angle in radians is

• A. $\frac{7\pi }{9}$
• B. $\frac{3\pi }{5}$
• C. $\frac{\pi }{2}$
• D. $\frac{\pi }{9}$

Answer 1

The correct option is C $\frac{\pi }{2}$

Let the angles of triangle be $x,2xand3x$ respectively.
We know that
Sum of all angles of triangle = ${180}^0$
$x+2x+3x={180}^0$
$6x={180}^0$
$x={30}^0$
Greatest angle = $3x=3\times 30={90}^0$
In radian = $\frac{\pi }{2}$