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

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(B) Let the angles of the triangle be $x, 2x, 3x$.Since the sum of angles in a triangle is $180^\circ$,we have $x + 2x + 3x = 180^\circ$,which gives $

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$1:\sqrt{3}:2$

Vedclass · Answer

(B) Let the angles of the triangle be $x, 2x, 3x$.Since the sum of angles in a triangle is $180^\circ$,we have $x + 2x + 3x = 180^\circ$,which gives $6x = 180^\circ$,so $x = 30^\circ$.The angles are $30^\circ, 60^\circ, 90^\circ$.By the Sine Rule,the sides $a, b, c$ are proportional to the sines of their opposite angles:$a:b:c = \sin(30^\circ) : \sin(60^\circ) : \sin(90^\circ)$.Substituting the values,we get $a:b:c = \frac{1}{2} : \frac{\sqrt{3}}{2} : 1$.Multiplying by $2$,we get $a:b:c = 1 : \sqrt{3} : 2$.

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

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