Trigonometric Equations Question 287
Question: The ratio of the sides of triangle ABC is $ 1:\sqrt{3}:2 $ . The ratio of $ A:B:C $ is
[IIT Screening 2004]
Options:
A) $ 3:5:2 $
B) $ 1:\sqrt{3}:2 $
C) 3 : 2 : 1
D) 1: 2 : 3
Show Answer
Answer:
Correct Answer: D
Solution:
- We have $ a:b:c=1:\sqrt{3}:2 $ i.e, $ a=\lambda ,,b=\sqrt{3}\lambda ,,c=2\lambda $ $ \cos A=\frac{3{{\lambda }^{2}}+4{{\lambda }^{2}}-{{\lambda }^{2}}}{2(\sqrt{3}\lambda )(2\lambda )}=\frac{6{{\lambda }^{2}}}{4\sqrt{3}{{\lambda }^{2}}}=\frac{\sqrt{3}}{2} $ $ \cos A=\frac{\sqrt{3}}{2} $
Þ $ A=30{}^\circ $ Similarly, $ \cos B=\frac{1}{2}\Rightarrow B=60{}^\circ $ , $ cos,C=0\Rightarrow C=90{}^\circ $ . Hence $ A:B:C=1:2:3 $ .
BETA
