Question

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

• A. $2\text{cm}$
• B. $5\text{cm}$
• C. $7\text{cm}$
• D. $10\text{cm}$

Answer 1

The correct option is D $10\text{cm}$

Let the angles be $2x,3x,7x$ $\Rightarrow 2x+3x+7x=180\Rightarrow x=15$
So, the angles are ${30}^{\circ },{45}^{\circ },{105}^{\circ }$

The smallest side is the one opposite to the smallest angle.
Using sine rule,
$\frac{a}{\sin A}=2R$
$\Rightarrow \frac{a}{\sin {30}^{\circ }}=2R$
$\Rightarrow 2a=2R$
$\Rightarrow a=R=10\text{cm}$