If `sinA=(3)/(4)`, then find the value of tan A.

Answer

To find the value of \( \tan A \) given that \( \sin A = \frac{3}{4} \), we can follow these steps:

### Step 1: Understand the definition of sine
The sine of an angle in a right triangle is defined as the ratio of the length of the opposite side (perpendicular) to the length of the hypotenuse.

### Step 2: Set up the triangle
Given \( \sin A = \frac{3}{4} \), we can interpret this in a right triangle:
- Let the length of the perpendicular side (BC) be 3.
- Let the length of the hypotenuse (AC) be 4.

### Step 3: Use the Pythagorean theorem to find the base
To find the length of the base (AB), we can use the Pythagorean theorem, which states:
\[ AC^2 = AB^2 + BC^2 \]
Substituting the known values:
\[ 4^2 = AB^2 + 3^2 \]
This simplifies to:
\[ 16 = AB^2 + 9 \]
Subtracting 9 from both sides gives:
\[ AB^2 = 16 - 9 = 7 \]
Taking the square root of both sides, we find:
\[ AB = \sqrt{7} \]

### Step 4: Calculate \( \tan A \)
The tangent of angle A is defined as the ratio of the opposite side (perpendicular) to the adjacent side (base):
\[ \tan A = \frac{BC}{AB} \]
Substituting the values we have:
\[ \tan A = \frac{3}{\sqrt{7}} \]

### Final Answer
Thus, the value of \( \tan A \) is:
\[ \tan A = \frac{3}{\sqrt{7}} \]