Question

The side of a triangle are in the ratio $1:\sqrt{3}:2$, then the angle of the triangle are in the ratio

• A. $1:3:5$
• B. $2:3:4$
• C. $3:2:1$
• D. $1:2:3$

Answer 1

The correct option is D $1:2:3$

Let $a=x,b=\sqrt{3}x,c=2x$
$c^2=a^2+b^2\Rightarrow \angle C={90}^0$

$tanA=\frac{1}{\sqrt{3}}\Rightarrow \angle A={30}^0$

$B={180}^0-(A+C)={180}^0-({90}^0+{30}^0)={60}^0$

$A:B:C=1:2:3$