If `tan A=(5)/(12)`, then the value of `cosA` is

Options

A. `(5)/(13)`
B. `(12)/(5)`
C. `(13)/(5)`
D. `(12)/(13)`.

Answer

To find the value of \( \cos A \) given that \( \tan A = \frac{5}{12} \), we can follow these steps:

### Step 1: Understand the relationship of tangent in a right triangle
Given that \( \tan A = \frac{\text{opposite}}{\text{adjacent}} \), we can assign the values:
- Opposite side (perpendicular) = 5
- Adjacent side (base) = 12

### Step 2: Use the Pythagorean theorem to find the hypotenuse
According to the Pythagorean theorem:
\[ h^2 = \text{opposite}^2 + \text{adjacent}^2 \]
Substituting the values we have:
\[ h^2 = 5^2 + 12^2 = 25 + 144 = 169 \]
Taking the square root to find \( h \):
\[ h = \sqrt{169} = 13 \]

### Step 3: Calculate \( \cos A \)
The cosine of angle \( A \) is given by the ratio of the adjacent side to the hypotenuse:
\[ \cos A = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{12}{13} \]

### Final Answer
Thus, the value of \( \cos A \) is \( \frac{12}{13} \).

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