If the angles of a triangle are in the ratio | vedclass

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(B) Let $	riangle ABC$ be a triangle such that $\angle A: \angle B: \angle C = 1: 2: 3$.Let the ratio constant be $x$,then $\angle A = x, \angle B =

Vedclass · Accepted Answer

$1: \sqrt{3}: 2$

Vedclass · Answer

(B) Let $	riangle ABC$ be a triangle such that $\angle A: \angle B: \angle C = 1: 2: 3$.Let the ratio constant be $x$,then $\angle A = x, \angle B = 2x, \angle C = 3x$.Using the angle sum property of a triangle:$\angle A + \angle B + \angle C = 180^{\circ}$$x + 2x + 3x = 180^{\circ}$ $\Rightarrow 6x = 180^{\circ}$ $\Rightarrow x = 30^{\circ}$.Thus,$\angle A = 30^{\circ}, \angle B = 60^{\circ}, \angle C = 90^{\circ}$.Using the sine rule,$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$:$\frac{a}{\sin 30^{\circ}} = \frac{b}{\sin 60^{\circ}} = \frac{c}{\sin 90^{\circ}}$$\frac{a}{1/2} = \frac{b}{\sqrt{3}/2} = \frac{c}{1}$Multiplying by $1/2$,we get $a: b: c = 1: \sqrt{3}: 2$.

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

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