Answer: [tex]cot \theta =\sqrt{ \frac{19}{6} }[/tex].
Step-by-step explanation: Given sinθ= √6/5.
We know radio of [tex]Sin\theta =\frac{Opposite \ side }{Hypotenuse}[/tex].
Therefore,
[tex]\frac{Opposite \ side }{Hypotenuse}= \frac{\sqrt{6} }{5}[/tex].
Let us apply Pythagoras Theorem to find the third side(Adjacent side) of the triangle .
[tex](a)^2 + (b)^2 = (c)^2.[/tex]
[tex](\sqrt{6})^2+(b)^2=(5)^2[/tex]
[tex]6+(b)^2 = 25[/tex]
Subtracting 6 from both sides, we get
[tex]6-6+(b)^2 = 25-6[/tex]
[tex](b)^2 = 19[/tex]
[tex]b=\sqrt{19}[/tex]
Therefore, adjacent side = [tex]\sqrt{19}[/tex]
We know,
[tex]cot \theta = \frac{Adjacent \ side}{Opposite \ side}[/tex]
[tex]cot \theta =\frac{\sqrt{19} }{\sqrt{6} }[/tex]
Or
[tex]cot \theta =\sqrt{ \frac{19}{6} }[/tex].
