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The problem is asking to find the angle \(\theta\) such that \(\sin(\theta) = 0.9769\), where \(\theta\) is between \(0^\circ\) and \(90^\circ\). The answer should be rounded to the nearest tenth of a degree.

To find \(\theta\), we use the inverse sine function (also known as arcsin or \(\sin^{-1}\)):

\[
\theta = \sin^{-1}(0.9769)
\]

Let me calculate that for you.The angle \(\theta\) that satisfies \(\sin(\theta) = 0.9769\) is approximately \(77.7^\circ\), rounded to the nearest tenth of a degree.

Do you need more details or have any questions?

Here are 5 related questions to expand on this:
1. How is the inverse sine function used to find angles in trigonometry?
2. What are the restrictions on the range of the inverse sine function?
3. How can the sine function be used to find angles in non-right triangles?
4. What other trigonometric functions have inverse operations, and how are they used?
5. How does the unit circle relate to the sine function?

**Tip**: Always ensure your calculator is set to the correct mode (degrees or radians) based on the problem's requirements!

Find θ if θ is between 0° and 90°. Round your answer to the nearest tenth of a degree. sin θ = 0.9769

Solve for θ when sin(θ) = 0.9769 and θ is between 0° and 90°. This trigonometry problem walks through using the inverse sine function to find the angle, rounding to the nearest tenth of a degree. Suitable for high school students.

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