Given : `sin A=(3)/5 ` , find :
cos A

Answer

To find \( \cos A \) given that \( \sin A = \frac{3}{5} \), we can follow these steps:

### Step 1: Understand the relationship of sine in a right triangle
We know that:
\[ \sin A = \frac{\text{Perpendicular}}{\text{Hypotenuse}} \]
Given \( \sin A = \frac{3}{5} \), we can identify:
- Perpendicular = 3
- Hypotenuse = 5

### Step 2: Draw a right triangle
Draw a right triangle where:
- Angle \( A \) is one of the angles.
- The side opposite to angle \( A \) (the perpendicular) is 3 units long.
- The hypotenuse is 5 units long.

### Step 3: Use the Pythagorean theorem to find the base
According to the Pythagorean theorem:
\[ \text{Hypotenuse}^2 = \text{Perpendicular}^2 + \text{Base}^2 \]
We can rearrange this to find the base:
\[ \text{Base}^2 = \text{Hypotenuse}^2 - \text{Perpendicular}^2 \]

### Step 4: Substitute the values
Substituting the known values:
\[ \text{Base}^2 = 5^2 - 3^2 \]
Calculating the squares:
\[ \text{Base}^2 = 25 - 9 = 16 \]

### Step 5: Find the base
Taking the square root to find the base:
\[ \text{Base} = \sqrt{16} = 4 \]

### Step 6: Calculate \( \cos A \)
Now that we have the base, we can find \( \cos A \):
\[ \cos A = \frac{\text{Base}}{\text{Hypotenuse}} = \frac{4}{5} \]

### Final Answer
Thus, the value of \( \cos A \) is:
\[ \cos A = \frac{4}{5} \]

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