Question

The angles of a triangle are in $A.P.$. The number of degree in the least is to be the number of radians in the greatest as $60:\pi$. Then the greatest angle is

• A. ${120}^0$
• B. ${90}^0$
• C. ${135}^0$
• D. ${105}^0$

Answer 1

The correct option is B ${90}^0$

Let tha angles of the triangle be ${(a-d)}^0,a^0,{(a+d)}^0$

Their sum $=a-d+a+a+d={180}^0\Rightarrow 3a={180}^0\Rightarrow a={60}^0$

Again by the given condition,

$\frac{a-d}{(a+d)\frac{\pi }{{180}^0}}=\frac{{60}^0}{\pi }\Rightarrow \frac{3(a-d)}{a+d}=1\Rightarrow 3a-3d=a+d\Rightarrow 2a=4d\Rightarrow a=2d\Rightarrow {60}^0=2d\Rightarrow {30}^0=d$

Hence, the greatest angle $={60}^0+{30}^0={90}^0$.