**Question:**

If the angles of a triangle are in the ratio 1 : 2 : 3, prove that its corresponding sides are in the ratio $1: \sqrt{3}: 2$

**Solution:**

Given: Angles of a triangle are in the ratio 1 : 2 : 3

Need to prove: Its corresponding sides are in the ratio $1: \sqrt{3}: 2$

Let the angles are $x, 2 x, 3 x$

Therefore, $x+2 x+3 x=180^{0}$

$6 x=180^{\circ}$

$x=30^{\circ}$

So, the angles are $30^{\circ}, 60^{\circ}, 90^{\circ}$

So, the ratio of the corresponding sides are:

$=\sin 30^{\circ}: \sin 60^{\circ}: \sin 90^{\circ}$

$=\frac{1}{2}: \frac{\sqrt{3}}{2}: 1$

$=1: \sqrt{3}: 2$ [Proved]