Question

What is the length of the third side in the above triangle? [2 Marks]

Answer 1

From Pythagoras theorem, we have

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

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

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

[1 Mark]

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

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

$oppositeside=cot\theta$ [1 Mark]