Question

The value of $\tan$ ${45}^{\circ }$ is

• A. √2
• B. 1
• C. 1/√3
• D. √3

Answer 1

The correct option is B

1

Consider the right isosceles triangle $\Delta ABC$ in figure having base and perpendicular AB and BC respectively of 1 unit length each.
$\therefore AC=\sqrt{{AB}^2+{BC}^2}=\sqrt{1^2+1^2}=\sqrt{2}Sincethe\Delta isisosceles,\angle CAB=\angle ACBalso\angle CAB+\angle ACB+\angle ABC={180}^{\circ }\Rightarrow \angle CAB+\angle ACB+{90}^{\circ }={180}^{\circ }\Rightarrow \angle CAB=\angle ACB={45}^{\circ }$

$tan\angle CAB=tan{45}^{\circ }=\frac{CB}{AB}=1$