ABCD is a square field with AB = x. A vertical pole OP of height 2x stands at the centre O of the square field. If ∠APO = θ, then what is cot θ equal to ? 

Given:

AB = x

∠APO = θ

Concept used:

Diagonal of square = √2a

cotθ = base/perpendicular

Calculation:

According to the above concept,

Diagonal of square = √2a

⇒ AC = x√2

⇒ OA = \(\frac{x√2}{{2}}\) = \(\frac{x}{{√2}}\)

Now, according to the above figure,

In ΔOAP,

⇒ cotθ = \(\frac{OP}{{OA}}\) = \(\frac{2x}{{x/√ 2}}\)

⇒ cotθ = 2√2

∴ The required value of cotθ is 2√2