Question

If angles of triangle $ABC$ are in ratio $1:2:3,$ then the ratio of their corresponding sides is

• A. $1:2:3$
• B. $3:2:1$
• C. $\sqrt{3}:2:1$
• D. $1:\sqrt{3}:2$

Answer 1

The correct option is D $1:\sqrt{3}:2$

Given : for triangle $ABC$
$A:B:C=1:2:3$
Also, $A+B+C=\pi$
$\Rightarrow \angle A={30}^{\circ },\angle B={60}^{\circ },\angle C={90}^{\circ }$
using sine rule :
$\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\Rightarrow \frac{a}{c}=\frac{\sin A}{\sin C}=\frac{1}{2}$
and $\frac{a}{b}=\frac{\sin A}{\sin B}$
$\Rightarrow \frac{a}{b}=\frac{1}{\sqrt{3}}\therefore a:b:c=1:\sqrt{3}:2$