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

Answer

To find \( \tan A \) 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:
\[ \sin A = \frac{\text{Perpendicular}}{\text{Hypotenuse}} \]
From the given information, we have:
\[ \sin A = \frac{3}{5} \]
This tells us that the length of the perpendicular side (opposite to angle A) is 3 and the length of the hypotenuse is 5.

### Step 2: Draw a right triangle
Draw a right triangle \( ABC \) where:
- \( \angle A \) is one of the angles,
- \( \angle B \) is the right angle (90 degrees),
- The side opposite \( \angle A \) (perpendicular) is 3,
- The hypotenuse is 5.

### 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:
\[ \text{Base}^2 = \text{Hypotenuse}^2 - \text{Perpendicular}^2 \]
Substituting the known values:
\[ \text{Base}^2 = 5^2 - 3^2 \]
Calculating the squares:
\[ \text{Base}^2 = 25 - 9 \]
\[ \text{Base}^2 = 16 \]
Taking the square root to find the base:
\[ \text{Base} = \sqrt{16} = 4 \]

### Step 4: Calculate \( \tan A \)
Now that we have both the perpendicular and the base, we can find \( \tan A \):
\[ \tan A = \frac{\text{Perpendicular}}{\text{Base}} = \frac{3}{4} \]

### Final Answer
Thus, the value of \( \tan A \) is:
\[ \tan A = \frac{3}{4} \]

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