Question

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

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

Answer 1

The correct option is C $\cot \theta$

From Pythagoras theorem, we have

$(adjacentside{)}^2+(oppositeside{)}^2=(hypotenuse{)}^2$

$oppositeside=\sqrt{(hypotenuse{)}^2-(adjacentside{)}^2}$

$oppositeside=\sqrt{(cosec\theta {)}^2-(1{)}^2}$

As we know, $(cosec\theta {)}^2-(1{)}^2=co{t}^2\theta$

$oppositeside=\sqrt{co{t}^2\theta }$

$oppositeside=cot\theta$