JEE Main & Advanced Mathematics Triangles & Properties of Triangle Question Bank Self Evaluation Test - Properties of Triangles and Height & Dstances

In a triangle ABC, \[c=2,A=45{}^\circ ,a=2\sqrt{2}\], than what is C equal to?

A) \[30{}^\circ \]

B) \[15{}^\circ \]

C) \[45{}^\circ \]

D) None of these

Correct Answer: A

Solution :

[a] According to sine rule,

\[\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\]

\[\therefore \frac{a}{\sin A}=\frac{c}{\sin C}\]

\[\Rightarrow \sin C=\frac{c.\sin A}{a}=\frac{2.\sin 45{}^\circ }{2\sqrt{2}}\]

\[=\frac{1}{\sqrt{2}}.\frac{1}{\sqrt{2}}=\frac{1}{2}=\sin 30{}^\circ \]

\[\therefore C=30{}^\circ \]