In `DeltaABC`, right angled at B, AB = 24 cm, BC = 7 cm. The value of `cos A` is :

Options

A. `(7)/(25)`
B. `(24)/(25)`
C. `(7)/(24)`
D. None of these

Answer

To find the value of \( \cos A \) in triangle \( \Delta ABC \) which is right-angled at \( B \), we can follow these steps:

### Step 1: Identify the sides of the triangle
In triangle \( \Delta ABC \):
- \( AB = 24 \, \text{cm} \) (Adjacent side to angle \( A \))
- \( BC = 7 \, \text{cm} \) (Opposite side to angle \( A \))

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

### Step 3: Calculate \( \cos A \)
The cosine of angle \( A \) is defined as the ratio of the length of the adjacent side to the hypotenuse:
\[ \cos A = \frac{AB}{AC} \]
Substituting the values we found:
\[ \cos A = \frac{24}{25} \]

### Final Answer
Thus, the value of \( \cos A \) is:
\[ \cos A = \frac{24}{25} \]

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