The angles of a triangle are in the ratio 2:3 | vedclass

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(D) Let the angles of the triangle be $2x, 3x,$ and $7x$.Since the sum of angles in a triangle is $180^{\circ}$, we have $2x + 3x + 7x = 180^{\circ}$.

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$10$

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(D) Let the angles of the triangle be $2x, 3x,$ and $7x$.Since the sum of angles in a triangle is $180^{\circ}$, we have $2x + 3x + 7x = 180^{\circ}$.$12x = 180^{\circ} \Rightarrow x = 15^{\circ}$.Thus, the angles are $30^{\circ}, 45^{\circ},$ and $105^{\circ}$.The smallest side $a$ is opposite to the smallest angle $30^{\circ}$.Using the Sine Rule, $\frac{a}{\sin A} = 2R$, where $R = 10 	ext{ cm}$.$\frac{a}{\sin 30^{\circ}} = 2 	imes 10$.$a = 20 	imes \frac{1}{2} = 10 	ext{ cm}$.

The angles of a triangle are in the ratio $2:3:7$ and the radius of the circumscribed circle is $10 \text{ cm}$. The length of the smallest side is (in $\text{ cm}$)

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