Question

If the angles of a triangle are in the ratio 3 : 4 : 5, then the sides are in the ratio

• A.
• B.
• C.
• D. 3 : 4 :5

Answer 1

The correct option is A

Let the angles of a triangle are $3\theta ,4\theta ,5\theta$

$\therefore 30+40+50={180}^0\Rightarrow \theta ={15}^0\therefore \text{Angles are}{45}^0,{60}^0,{75}^{0}Now,sinA=sin{45}^0=\frac{1}{\sqrt{2}}sinB=sin{60}^0=\frac{\sqrt{3}}{2}sinC=sin{75}^0=\frac{\sqrt{3}+1}{2\sqrt{2}}\therefore a:b:c=sinA:sinB:sinC\frac{1}{\sqrt{2}}:\frac{\sqrt{3}}{2}:\frac{\sqrt{3}+1}{2\sqrt{2}}=2:\sqrt{6}:\sqrt{3}+1$