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The given problem asks to find a value of \( \alpha \) in the interval \([0^\circ, 90^\circ]\) that satisfies the equation:

\[
\cot(\alpha) = 1.4022781
\]

### Solution:

1. The cotangent function is the reciprocal of the tangent function, so:
   \[
   \cot(\alpha) = \frac{1}{\tan(\alpha)}
   \]

2. To solve for \( \alpha \), we take the reciprocal of \( \cot(\alpha) \):
   \[
   \tan(\alpha) = \frac{1}{\cot(\alpha)} = \frac{1}{1.4022781}
   \]

   Let's calculate this value first.

3. Now, to find \( \alpha \), we take the arctangent (inverse tangent) of the result.

I'll calculate this now.The value of \( \alpha \) that satisfies the equation \( \cot(\alpha) = 1.4022781 \) in the interval \([0^\circ, 90^\circ]\) is approximately:

\[
\alpha \approx 35.493629^\circ
\]

Would you like further details or explanations?

Here are some related questions:
1. What is the definition of the cotangent function?
2. How does the arctangent function work for angles?
3. Why is \( \alpha \) restricted to the interval \([0^\circ, 90^\circ]\)?
4. How can you verify this value using a calculator?
5. What other angles have the same cotangent value outside this interval?

**Tip**: Always check your calculator's settings (degrees vs. radians) when working with trigonometric functions.

Find a value of α in the interval [0°, 90°] that satisfies cot α = 1.4022781.

Learn how to find the value of α in the interval [0°, 90°] that satisfies the equation cot α = 1.4022781 using inverse trigonometric functions and reciprocal identities. This problem is ideal for high school students in Grades 9-12.

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