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. 1:03:05
• B. 2:03:02
• C. 3:02:01
• D. 1:02:03

Answer 1

Answer: (D)

1:02:03

Answer 2

Let a : b : c = 1 : $\sqrt 3 : 2 \Rightarrow c^2 = a^2 + b^2$
$\therefore$ Triangle is right angled at C
or $\angle C = 90^ \circ \, and \, \frac{a}{b} = \frac{1}{\sqrt 3}$
In $\triangle BAC, \, tan \, A = \frac{a}{b} = \frac{1}{\sqrt 3}$
$\Rightarrow A = 30^ \circ \, and \, B = 60^\circ$
\hspace29mm $[ \because A + B = 90^\circ ]$
$\therefore$ Ratio of angles, A :B : C = $30^\circ : 60^\circ : 90^\circ$
= 1 : 2 : 3