Triangles And Properties Of Triangle Question 28
Question: In a triangle ABC, $ c=2,A=45{}^\circ ,a=2\sqrt{2} $ , than what is C equal to?
Options:
A) $ 30{}^\circ $
B) $ 15{}^\circ $
C) $ 45{}^\circ $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
[a] According to sine rule, $ \frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C} $
$ \therefore \frac{a}{\sin A}=\frac{c}{\sin C} $
$ \Rightarrow \sin C=\frac{c.\sin A}{a}=\frac{2.\sin 45{}^\circ }{2\sqrt{2}} $ $ =\frac{1}{\sqrt{2}}.\frac{1}{\sqrt{2}}=\frac{1}{2}=\sin 30{}^\circ $
$ \therefore C=30{}^\circ $
BETA
