If `sin A=(5)/(13)`, then the value of `secA` is :

Options

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

Answer

To find the value of \( \sec A \) given that \( \sin A = \frac{5}{13} \), we can follow these steps:

### Step 1: Understand the relationship between sine and secant
We know that:
\[ \sin A = \frac{\text{Opposite}}{\text{Hypotenuse}} \]
In this case, we have:
- Opposite side = 5
- Hypotenuse = 13

### Step 2: Use the Pythagorean theorem to find the adjacent side
According to the Pythagorean theorem:
\[ \text{Hypotenuse}^2 = \text{Opposite}^2 + \text{Adjacent}^2 \]
Substituting the known values:
\[ 13^2 = 5^2 + \text{Adjacent}^2 \]
Calculating the squares:
\[ 169 = 25 + \text{Adjacent}^2 \]
Now, isolate the adjacent side:
\[ \text{Adjacent}^2 = 169 - 25 \]
\[ \text{Adjacent}^2 = 144 \]
Taking the square root:
\[ \text{Adjacent} = \sqrt{144} = 12 \]

### Step 3: Calculate secant
Now, we can find \( \sec A \):
\[ \sec A = \frac{\text{Hypotenuse}}{\text{Adjacent}} = \frac{13}{12} \]

### Final Answer
Thus, the value of \( \sec A \) is:
\[ \sec A = \frac{13}{12} \]

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