In a triangle ABC, side c = 2, angle A = 45°, side \({\rm{a}} = 2\sqrt 2 \), then what is angle C equal to?

Concept:

In triangle ABC, According to Sine rule

\(\frac{a}{\text{sinA}}=\frac{b}{\text{sinB}}=\frac{c}{\text{sinC}}\) Where, a, b, c are sides and A, B, C are angles of triangle.

Calculation:

In a triangle ABC, c = 2, A = 45°, \({\rm{a}} = 2\sqrt 2 \),

Using sine rule in given triangle,

 \(\frac{a}{\text{sinA}}=\frac{c}{\text{sinC}}\\ \Rightarrow \frac{2\sqrt2}{\text{sin45}}=\frac{2}{\text{sinC}}\\\Rightarrow \text{sinC} = \frac{\text{sin45}}{\sqrt2}=\frac{1}{\sqrt2\sqrt2}\\ \Rightarrow \text{sinC} =\frac{1}{2}\\ \Rightarrow C =30\)

Hence, option (1) is correct.