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The problem asks to find the angle \(\theta\) given that \(\cos \theta = 0.8265\) in the interval \([270^\circ, 360^\circ)\).

### Step 1: Determine the Quadrant
The interval \([270^\circ, 360^\circ)\) corresponds to the fourth quadrant.

### Step 2: Use the Inverse Cosine Function
To find \(\theta\), use the inverse cosine function:
\[
\theta = \cos^{-1}(0.8265)
\]
Using a calculator or an appropriate tool, find the angle in degrees.

\[
\theta = \cos^{-1}(0.8265) \approx 34.0^\circ
\]

### Step 3: Adjust for the Fourth Quadrant
Since \(\theta\) is in the fourth quadrant, the actual angle is:
\[
\theta = 360^\circ - 34.0^\circ = 326.0^\circ
\]

### Conclusion:
The correct answer, rounded to the nearest hundredth, is approximately \( \boxed{326.00^\circ} \).

Would you like to ask any further questions or need more details?

Here are 5 related questions for further practice:
1. What is the value of \(\sin \theta\) when \(\cos \theta = 0.5\) and \(\theta\) is in the third quadrant?
2. How do you calculate the reference angle in any quadrant?
3. What is the exact value of \(\theta\) if \(\cos \theta = -\frac{1}{2}\) in the interval \([180^\circ, 270^\circ)\)?
4. How can you determine the angle in degrees if given \(\sin \theta = 0.5\) and the interval is \([0^\circ, 180^\circ)\)?
5. What are the properties of the cosine function in different quadrants?

**Tip:** Always

Learn how to find the angle \( \theta \) given that \( \cos \theta = 0.8265 \) in the interval \([270^\circ, 360^\circ)\). This trigonometry problem involves using the inverse cosine function and adjusting for the fourth quadrant. Suitable for high school students studying trigonometry.

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