Question

Given that $\sin A=\frac{1}{2}$ and $\cos B=\frac{1}{\sqrt{2}}$, where $A$ and $B$ are acute angles, then the value of $A+B$ is:

• A. ${30}^o$
• B. ${45}^o$
• C. ${75}^o$
• D. ${15}^o$

Answer 1

Answer: (C)

${75}^o$

Given, $\sin A=\frac{1}{2}$

$\Rightarrow \sin A=\sin 30(\sin 30=\frac{1}{2})$

$\Rightarrow A=30$

Also given $\cos B=\frac{1}{\sqrt{2}}$

$\Rightarrow \cos B=\cos 45(\cos 45=\frac{1}{\sqrt{2}})$

$\Rightarrow B=45$

Therefore, $A+B=30+45=75$