Question

The sides of a triangle are in the ratio $1:$ $\sqrt{3}$ $:2$, then the angles 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 $a=x,b=\sqrt{3}x,c=2x$
Clearly $c^2=a^2+b^2\Rightarrow \angle C={90}^0$
$\tan A=\frac{a}{b}=\frac{1}{\sqrt{3}}\Rightarrow \angle A={30}^0$.
$\Rightarrow A$ : $B$ : $C=1$ : 2 : 3.