A) \[\frac{\sqrt{3}}{2}\]
B) \[\frac{\sqrt{3}+1}{2\sqrt{2}}\]
C) \[\frac{\sqrt{3}+1}{2}\]
D) \[\frac{\sqrt{3}+1}{\sqrt{2}}\]
E) \[\frac{\sqrt{3}}{2\sqrt{2}}\]
Correct Answer: C
Solution :
Let \[A=3\theta ,B=4\theta ,C=5\theta \] \[\Rightarrow \] \[\Rightarrow A+B+C=3\theta +4\theta +5\theta =12\theta ={{180}^{\text{o}}}\] \[\Rightarrow \] \[\theta =\frac{180{}^\circ }{12}=\frac{\pi }{12}\] \[\therefore \] \[A=\frac{3\pi }{12}=\frac{\pi }{4}\] \[B=\frac{4\pi }{12}=\frac{\pi }{3}\] and \[C=\frac{5\pi }{12}\] \[\therefore \] \[a=\sin \frac{\pi }{4}=\frac{1}{\sqrt{2}},b=\sin \frac{\pi }{3}=\frac{\sqrt{3}}{2}\] \[c=\sin \left( \frac{\pi }{2}-\frac{\pi }{12} \right)\] \[=\cos \frac{\pi }{12}=\frac{\sqrt{3}+1}{2\sqrt{2}}\] \[\therefore \]Required ratio\[=\frac{\frac{\frac{\sqrt{3}+1}{2\sqrt{2}}}{1}}{\sqrt{2}}=\frac{\sqrt{3}+1}{2}\]
You need to login to perform this action.
You will be redirected in
3 sec
