Question

The ratio of the sides of triangle ABC is $1:\sqrt{3}:2$.The ratio of A:B:C is

• A. $3:5:2$
• B. $1:\sqrt{3}:2$
• C. $3:2:1$
• D. $1:2:3$

Answer 1

Answer: (D)

$1:2:3$

$a:b:c=1:\sqrt{3}:2$

Therefore,

$a=k$

$b=\sqrt{3}k$

$c=2k$

$a^2+b^2=k^2+{\left(\sqrt{3}k\right)}^2=4k^2$

$c^2={\left(2k\right)}^2=4k^2$

$\Rightarrow a^2+b^2=c^2$

Thus, $△ABC$ is a right angled triangle, where $\angle C=90$.

Now,

$\tan A=\frac{a}{b}=\frac{1}{\sqrt{3}}=\tan 30$

$\Rightarrow \angle A=30$

$\Rightarrow \angle B=180-90-30=60$

Therefore,

$\angle A:\angle B:\angle C=30:60:90=1:2:3$