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

Concept:

Sine rule: \(\frac{a}{{\sin A}} = \frac{b}{{\sin B}} = \frac{c}{{\sin C}}\)

Calculation:

Given: The angles of a triangle ABC are in the ratio 1 : 2 : 3

Let, ∠ A = x, ∠ B = 2x and ∠ C = 3x

⇒ ∠ A + ∠ B + ∠ C = 180°     ...(By angle sum property)

⇒ x = 30°

⇒ ∠ A = 30°, ∠ B = 60° and ∠ C = 90°

As we know that, \(\frac{a}{{\sin A}} = \frac{b}{{\sin B}} = \frac{c}{{\sin C}}\)

\(\Rightarrow \;\frac{a}{{\sin 30^\circ }} = \frac{b}{{\sin 60^\circ }} = \frac{c}{{sin \ 90^\circ }} = k\)

⇒ a = k/2, b = √3 k/2 and c = k