Trigonometric Equations Question 296
Question: In $ \Delta ABC $ if $ a=2,b=4 $ and $ \angle C=60^{o} $ , then $ \angle A $ and $ \angle B $ are equal to
Options:
A) $ 90^{o},30^{o} $
B) $ 60^{o},60^{o} $
C) $ 30^{o},90^{o} $
D) $ 60^{o},45^{o} $
Show Answer
Answer:
Correct Answer: C
Solution:
- Given, $ C=60^{o},a=2,b=4 $
Þ $ \cos C=\frac{a^{2}+b^{2}-c^{2}}{2ab} $ or $ ab=a^{2}+b^{2}-c^{2} $
Þ $ 8=4+16-c^{2} $ Þ $ c^{2}=12\Rightarrow c=\sqrt{12}=2\sqrt{3} $ . Þ $ \sin A=\frac{a\sin C}{c}=\frac{2\text{. }\frac{\sqrt{3}}{2}}{2\sqrt{3}}=\frac{1}{2}\Rightarrow A=\frac{\pi }{6} $ and $ \sin B=\frac{b\sin C}{c}=\frac{4\text{. }\frac{\sqrt{3}}{2}}{2\sqrt{3}}=1 $
Þ $ B=\frac{\pi }{2} $ .
BETA
