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 $=A:B:C$
$=30^{\circ }:60^{\circ }:90^{\circ }=1:2:3$