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To solve for \( \csc A \) in this right triangle, we first need to recall the definition of the cosecant function in trigonometry. 

In a right triangle:
\[
\csc A = \frac{\text{hypotenuse}}{\text{opposite side to } A}
\]

### Step-by-Step Solution

1. **Identify the sides**:
   - The hypotenuse is the longest side, labeled as \( 5 \).
   - The side opposite angle \( A \) is \( 3 \).
   - The side adjacent to angle \( A \) is \( 4 \).

2. **Apply the cosecant definition**:
   \[
   \csc A = \frac{\text{hypotenuse}}{\text{opposite}} = \frac{5}{3}
   \]

### Final Answer:
\[
\csc A = \frac{5}{3}
\]

Would you like further details on this solution or have any questions?

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Here are five related questions to expand your understanding:

1. How would you find \(\sin A\), \(\cos A\), and \(\tan A\) for the same triangle?
2. How can you verify if the triangle is a right triangle using the side lengths?
3. What is the relationship between \(\csc A\) and \(\sin A\)?
4. How would you calculate \(\cot A\) using these sides?
5. What are the values of \(\sec A\) and \(\csc A\) if the hypotenuse was a different length?

**Tip**: Remember, \(\csc A\) is the reciprocal of \(\sin A\). So once you know \(\sin A\), finding \(\csc A\) is straightforward!

Find csc A for the right triangle with sides 3, 4, and hypotenuse 5.

Learn how to find csc A for a right triangle with sides of length 3, 4, and hypotenuse 5. This solution explains the cosecant function in trigonometry and uses the Pythagorean Theorem. Suitable for students in Grades 9-10.

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