Question

In right angle $△ABC,\angle B={90}^o,\angle A={45}^o$, then $\sin {45}^o=$

• A. $1$
• B. $\sqrt{2}$
• C. $\frac{1}{\sqrt{2}}$
• D. None of above

Answer 1

Answer: (C)

$\frac{1}{\sqrt{2}}$

Given $\angle A={45}^o,\angle B={90}^o$

$\therefore \angle C={90}^o$

$\angle A=\angle C\Rightarrow AB=BC=a$

$AC=\sqrt{{AB}^2+{BC}^2}=\sqrt{a^2+a^2}=\sqrt{2a^2}=\sqrt{2}a$

$\sin {45}^o=\frac{BC}{AC}=\frac{a}{\sqrt{2}a}=\frac{1}{\sqrt{2}}$

So, $\frac{1}{\sqrt{2}}$ is correct.