Question

If the angles of a triangle are in the ratio 1:2:3, then the ratio of its corresponding sides is .

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

Answer 1

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

Let the angles of the triangle be x, 2x and 3x.
Then, x+2x+3x=360$°$.
So, the angles are 30$°$, 60$°$ and 90$°$.
Let a, b and c be the sides opposite to these angles.
Then,
$\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\Rightarrow a:b:c=\sin 30°:\sin 60°:\sin 90°\Rightarrow a:b:c=\frac{1}{2}:\frac{\sqrt{3}}{2}:1=1:\sqrt{3}:2$