Question

The sides of triangle are in the ratio $1 : \sqrt{3} : 2$, then the angles of the triangle are in ratio

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

Answer 1

Answer: (D)

Given, $a : b : c=1 : \sqrt{3} : 2$
Here, $c^{2}=a^{2}+b^{2}$

$\therefore \Delta$ is right angled at $C$.
$\therefore \angle C=90^{\circ}$ and $\frac{a}{b}=\frac{1}{\sqrt{3}}$
$\Rightarrow \tan A=\frac{1}{\sqrt{3}}$
$\Rightarrow A=30^{\circ}$ and $B=60^{\circ} \,\,\,[$ as $A+B=90^{\circ}]$
$\therefore $ Ratio of angles $=A: B: C$
$=30^{\circ}: 60^{\circ}: 90^{\circ}=1: 2: 3$