Find the Cotangent Given the Point (2 square root of 5,4)

$(2 \sqrt{5}, 4)$

To find the $\cot (θ)$ between the x-axis and the line between the points $(0, 0)$ and $(2 \sqrt{5}, 4)$ , draw the triangle between the three points $(0, 0)$ , $(2 \sqrt{5}, 0)$ , and $(2 \sqrt{5}, 4)$ .

Opposite : $4$

Adjacent : $2 \sqrt{5}$

$\cot (θ) = \frac{Adjacent}{Opposite}$ therefore $\cot (θ) = \frac{2 \sqrt{5}}{4}$ .

$\frac{2 \sqrt{5}}{4}$

Cancel the common factor of $2$ and $4$ .

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Factor $2$ out of $2 \sqrt{5}$ .

$\cot (θ) = \frac{2 (\sqrt{5})}{4}$

Cancel the common factors.

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Factor $2$ out of $4$ .

$\cot (θ) = \frac{2 \sqrt{5}}{2 \cdot 2}$

Cancel the common factor.

$\cot (θ) = \frac{2 \sqrt{5}}{2 \cdot 2}$

Rewrite the expression.

$\cot (θ) = \frac{\sqrt{5}}{2}$

Approximate the result.

$\cot (θ) = \frac{\sqrt{5}}{2} \approx 1.11803398$

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