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In a triangle $A B C$, side $\mathrm{C}=2$, angle $\mathrm{A}=45^{\circ}$, side $\mathrm{a}=2 \sqrt{2}$, then what is angle $\mathrm{C}$ equal to?
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Verified Answer
The correct answer is:
$30^{\circ}$
In a triangle
Using sine rule in given triangle,
$A B C, c=2, A=45^{\circ}, \mathrm{a}=2 \sqrt{2}$,
$\frac{a}{\sin \mathrm{A}}=\frac{c}{\sin \mathrm{C}} \Rightarrow \frac{2 \sqrt{2}}{\sin 45}=\frac{2}{\sin \mathrm{C}} \Rightarrow \sin \mathrm{C}=\frac{\sin 45}{\sqrt{2}}=\frac{1}{\sqrt{2} \sqrt{2}} \Rightarrow \sin \mathrm{C}=\frac{1}{2} \Rightarrow C=30$
Hence, option (1) is correct.
Using sine rule in given triangle,
$A B C, c=2, A=45^{\circ}, \mathrm{a}=2 \sqrt{2}$,
$\frac{a}{\sin \mathrm{A}}=\frac{c}{\sin \mathrm{C}} \Rightarrow \frac{2 \sqrt{2}}{\sin 45}=\frac{2}{\sin \mathrm{C}} \Rightarrow \sin \mathrm{C}=\frac{\sin 45}{\sqrt{2}}=\frac{1}{\sqrt{2} \sqrt{2}} \Rightarrow \sin \mathrm{C}=\frac{1}{2} \Rightarrow C=30$
Hence, option (1) is correct.
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