Trigonometric Equations Question 220
Question: In a $ \Delta ABC $ , $ b=2,C=60^{o},c=\sqrt{6} $ , then a =
Options:
A) $ \sqrt{3}-1 $
B) $ \sqrt{3} $
C) $ \sqrt{3}+1 $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
- We have $ \frac{b}{\sin B}=\frac{c}{\sin C} $
Þ $ \sin B=\frac{b\sin C}{c} $
Þ $ \sin B=\frac{2\sin 60^{o}}{\sqrt{6}}=\frac{2}{\sqrt{6}}.\frac{\sqrt{3}}{2}=\frac{1}{\sqrt{2}} $ Þ $ B=45^{o} $ , $ (\because B\ne 135^{o}) $ \ $ A=180^{o}-(B+C)=75^{o} $ Now $ \frac{\sin A}{a}=\frac{\sin B}{b} $ Þ $ a=\frac{b\sin A}{\sin B}=\frac{2\sin 75^{o}}{\sin 45^{o}}=\sqrt{3}+1 $ .
BETA
