In `Delta ABC`, right angled at `B, AB = 24 cm. BC=7 cm.` Determine ` sin A`.

Answer

To determine \( \sin A \) in triangle \( ABC \) which is right-angled at \( B \), we can follow these steps:

### Step 1: Identify the sides of the triangle
In triangle \( ABC \):
- \( AB \) is the side opposite angle \( C \) and is given as \( 24 \, \text{cm} \).
- \( BC \) is the side opposite angle \( A \) and is given as \( 7 \, \text{cm} \).
- \( AC \) is the hypotenuse which we need to calculate.

### Step 2: Use the Pythagorean theorem to find the hypotenuse
According to the Pythagorean theorem:
\[ AC^2 = AB^2 + BC^2 \]
Substituting the values:
\[ AC^2 = 24^2 + 7^2 \]
Calculating the squares:
\[ AC^2 = 576 + 49 \]
\[ AC^2 = 625 \]
Taking the square root to find \( AC \):
\[ AC = \sqrt{625} = 25 \, \text{cm} \]

### Step 3: Calculate \( \sin A \)
The sine of angle \( A \) is defined as the ratio of the length of the side opposite angle \( A \) (which is \( BC \)) to the length of the hypotenuse \( AC \):
\[ \sin A = \frac{BC}{AC} \]
Substituting the values we found:
\[ \sin A = \frac{7}{25} \]

### Final Answer
Thus, the value of \( \sin A \) is:
\[ \sin A = \frac{7}{25} \]