Question

What is the length of the third side in the above triangle?

• A. $\tan \theta$
• B. $\cot \theta$
• C. $\sec \theta$
• D. $\cos \theta$

Answer 1

The correct option is B

$\cot \theta$

From Pythagoras theorem, we have

$B{C}^2+A{C}^2=A{B}^2$

$\Rightarrow A{C}^2=A{B}^2-B{C}^2$
$\Rightarrow AC=\sqrt{(cosec\theta {)}^2-1^2}$
As we know, $cose{c}^2\theta -1={\cot }^2\theta$
$\Rightarrow AC=\sqrt{{\cot }^2\theta }$
$=\cot \theta$