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Question

(C) Given that the angles of a triangle are in the ratio $1: 2: 3$. From the angle sum property,the sum of all angles of a triangle is $180^{\circ}$.

Vedclass · Accepted Answer

$1: \sqrt{3}: 2$

Vedclass · Answer

(C) Given that the angles of a triangle are in the ratio $1: 2: 3$. From the angle sum property,the sum of all angles of a triangle is $180^{\circ}$. Let the angles be $x, 2x, 3x$. Then $x + 2x + 3x = 180^{\circ}$ $\Rightarrow 6x = 180^{\circ}$ $\Rightarrow x = 30^{\circ}$. So,the angles are $A = 30^{\circ}, B = 60^{\circ}, C = 90^{\circ}$. According to the sine rule,$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$. Substituting the values: $\frac{a}{\sin 30^{\circ}} = \frac{b}{\sin 60^{\circ}} = \frac{c}{\sin 90^{\circ}}$. $\Rightarrow \frac{a}{1/2} = \frac{b}{\sqrt{3}/2} = \frac{c}{1}$. Multiplying by $1/2$,we get $a : b : c = 1 : \sqrt{3} : 2$.

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

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