Let's work through the three problems you requested:

21. sin A = 0.5
To find angle $A$, we use the inverse sine function:
$A = \sin^{-1}(0.5)$ Using a calculator,
$A \approx 30.0^\circ$

23. cos A = 0.33
To find angle $A$, we use the inverse cosine function:
$A = \cos^{-1}(0.33)$ Using a calculator,
$A \approx 70.5^\circ$

25. tan A = 1.0
To find angle $A$, we use the inverse tangent function:
$A = \tan^{-1}(1.0)$ Using a calculator,
$A \approx 45.0^\circ$

Let me know if you'd like further explanation or have additional questions!

Further questions:

1. What are the relationships between the trigonometric ratios and the sides of a right triangle?
2. How can you verify trigonometric values using a calculator?
3. Can you calculate the other angles in a right triangle if you know one angle and the sides?
4. How do inverse trigonometric functions differ from regular trigonometric functions?
5. What happens when the sine, cosine, or tangent values exceed the range of 1 or -1?

Tip: To calculate inverse trigonometric functions, make sure your calculator is set to the correct mode (degrees or radians) based on your problem.