Question

What is the length of the third side in the triangle shown below?

• 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

$(adjside{)}^2+(opp.side{)}^2=(hyp{)}^2$

$opp.side=\sqrt{(hyp{)}^2-(adjside{)}^2}$

$opp.side=\sqrt{(cosec\theta {)}^2-(1{)}^2}$

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

$opp.side=\sqrt{co{t}^2\theta }$

$opp.side=cot\theta$