The given problem asks for a decimal approximation of $\cot(247^\circ36')$.

To solve this:

1. Convert $36'$ (36 minutes) to degrees. Since $1'$ is equal to $\frac{1}{60}$ degrees: $36' = \frac{36}{60} = 0.6^\circ$

   Therefore, $247^\circ36'$ is equivalent to: $247^\circ + 0.6^\circ = 247.6^\circ$

2. Now, find the cotangent of $247.6^\circ$. Using a calculator: $\cot(247.6^\circ) = \frac{1}{\tan(247.6^\circ)}$ The tangent of $247.6^\circ$ is approximately $-0.45257909$.

3. Thus: $\cot(247.6^\circ) \approx \frac{1}{-0.45257909} \approx -2.20970138$

So, the decimal approximation is approximately: $\boxed{-2.20970138}$

Would you like more details or have any questions?

Related Questions:

1. How do you convert angles from degrees and minutes to decimal form?
2. What is the relationship between cotangent and tangent?
3. Why is the cotangent of an obtuse angle negative?
4. How can trigonometric functions be calculated using a calculator?
5. What are other ways to express angles (e.g., radians)?

Tip:

Always ensure your calculator is set to degrees when working with angles in degrees and minutes.