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

s i n θ

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c o t θ

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s e c θ

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c o s θ

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Solution

The correct option is B $c o t θ$
From Pythagoras theorem, we have

$(a d j a c e n t s i d e)^{2} + (o p p o s i t e s i d e)^{2} = (h y p o t e n u s e)^{2}$

$o p p o s i t e s i d e = \sqrt{(h y p o t e n u s e)^{2} - (a d j a c e n t s i d e)^{2}}$

$o p p o s i t e s i d e = \sqrt{(c o s e c θ)^{2} - (1)^{2}}$

As we know, $(c o s e c θ)^{2} - (1)^{2} = c o t^{2} θ$

$o p p o s i t e s i d e = \sqrt{c o t^{2} θ}$

$o p p o s i t e s i d e = c o t θ$

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