If `sin3A=1 and 0 le A le 90^(@)`, find :
sin A

Answer

To solve the problem, we need to find the value of \( \sin A \) given that \( \sin 3A = 1 \) and \( 0 \leq A \leq 90^\circ \).

### Step-by-Step Solution:

1. **Understanding the given equation**: We know that \( \sin 3A = 1 \). The sine function reaches its maximum value of 1 at specific angles.

2. **Finding the angle**: The sine function equals 1 at \( 90^\circ \) and at odd multiples of \( 90^\circ \). However, since \( 3A \) must be within the range of angles we are considering (and \( A \) must be between \( 0^\circ \) and \( 90^\circ \)), we can set:
\[ 3A = 90^\circ \]

3. **Solving for \( A \)**: To find \( A \), we divide both sides of the equation by 3:
\[ A = \frac{90^\circ}{3} = 30^\circ \]

4. **Finding \( \sin A \)**: Now that we have \( A = 30^\circ \), we need to find \( \sin A \):
\[ \sin A = \sin 30^\circ \]

5. **Using known values**: We know from trigonometric ratios that:
\[ \sin 30^\circ = \frac{1}{2} \]

6. **Final answer**: Therefore, the value of \( \sin A \) is:
\[ \sin A = \frac{1}{2} \]

### Summary:
The final answer is \( \sin A = \frac{1}{2} \).