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The value of \(\theta\) that satisfies \(\tan(\theta) = 0.72088702\) in the interval \([0^\circ, 90^\circ]\) is approximately:

\[
\theta \approx 35.787344^\circ
\]

You can round this to six decimal places as \(\theta \approx 35.787344^\circ\).

Do you want more details or have any questions?

Here are some related questions to consider:
1. What is the relationship between the tangent function and the unit circle?
2. How can you solve trigonometric equations for different intervals?
3. What other trigonometric functions could be used to verify this solution?
4. How does the tangent function behave as \(\theta\) approaches \(90^\circ\)?
5. What is the inverse tangent function and how is it used to find angles?

**Tip**: Always ensure that your calculator is set to the correct mode (degrees or radians) when solving trigonometric problems.

Find a value of θ in the interval [0°, 90°] that satisfies the given statement: tan(θ) = 0.72088702.

Learn how to find the value of θ where tan(θ) = 0.72088702 within the interval [0°, 90°]. This solution involves inverse trigonometric functions and understanding of angle measurement in degrees. Suitable for students in Grades 10-12.

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