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We are given:

\[
\sin A = \frac{11}{8}, \quad 0^\circ < A < 90^\circ
\]

We need to find \(\tan \frac{A}{2}\).

### Step 1: Ensure the value of \(\sin A\)
Since \(\sin A = \frac{11}{8}\), which is greater than 1, this seems incorrect because the sine of an angle is bounded by \(-1 \leq \sin A \leq 1\) for all real angles \(A\). Could you confirm the given information? If it's a typo, feel free to provide clarification.

If you meant \(\sin A = 0.8\) or another plausible value, I can continue with the solution for \(\tan \frac{A}{2}\). Let me know!

Would you like more details or have questions?

### Related Questions:
1. What is the correct value of \(\sin A\)?
2. How do you use the half-angle identity for tangent?
3. How is \(\sin A\) related to \(\tan A\) in trigonometry?
4. What are the properties of the sine function for angles less than 90°?
5. How do you compute \(\tan A\) using \(\sin A\) and \(\cos A\)?

### Tip:
Always double-check the values for trigonometric functions to ensure they fall within valid ranges for given angles.

Given: sin A = 11/8, 0° < A < 90°. Find: tan A/2.

Explore how to find tan(A/2) when given sin(A) = 11/8 using the half-angle identity for tangent. Understand the steps involved and key trigonometric concepts like the Pythagorean identity. This problem is suitable for students in Grades 10-12.

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