In `DeltaABC` , right - angled at B , AB = 24 cm , BC = 7 cm .
`sinC , cos C`

Answer

To solve the problem, we will find the values of \( \sin C \) and \( \cos C \) in triangle \( \Delta ABC \) which is right-angled at \( B \). The sides are given as \( AB = 24 \, \text{cm} \) and \( BC = 7 \, \text{cm} \).

### Step 1: Identify the sides of the triangle
In triangle \( ABC \):
- \( AB \) is the opposite side to angle \( C \).
- \( BC \) is the adjacent side to angle \( C \).
- \( AC \) is the hypotenuse.

### Step 2: Use the Pythagorean theorem to find \( AC \)
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:
\[ AC = \sqrt{625} = 25 \, \text{cm} \]

### Step 3: Calculate \( \sin C \)
The sine of angle \( C \) is defined as:
\[ \sin C = \frac{\text{Opposite}}{\text{Hypotenuse}} = \frac{AB}{AC} \]
Substituting the values:
\[ \sin C = \frac{24}{25} \]

### Step 4: Calculate \( \cos C \)
The cosine of angle \( C \) is defined as:
\[ \cos C = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{BC}{AC} \]
Substituting the values:
\[ \cos C = \frac{7}{25} \]

### Final Answers:
\[ \sin C = \frac{24}{25}, \quad \cos C = \frac{7}{25} \]

---