If `tanA = 4/3`, the value of sin A is:

Options

A. `4/5`
B. `3/4`
C. `5/3`
D. `7/5`

Answer

To find the value of \( \sin A \) given that \( \tan A = \frac{4}{3} \), we can use the definitions of trigonometric ratios in a right triangle.

### Step-by-Step Solution:

1. **Understanding the Tangent Ratio:**
\[ \tan A = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{BC}{AB} \]
Given \( \tan A = \frac{4}{3} \), we can assign:
- Opposite side (BC) = \( 4k \)
- Adjacent side (AB) = \( 3k \)

2. **Applying the Pythagorean Theorem:**
In a right triangle, the relationship between the sides is given by:
\[ AC^2 = AB^2 + BC^2 \]
Substituting the values we have:
\[ AC^2 = (3k)^2 + (4k)^2 \]
\[ AC^2 = 9k^2 + 16k^2 = 25k^2 \]
Therefore, taking the square root:
\[ AC = 5k \]

3. **Finding \( \sin A \):**
The sine ratio is defined as:
\[ \sin A = \frac{\text{Opposite}}{\text{Hypotenuse}} = \frac{BC}{AC} \]
Substituting the values we found:
\[ \sin A = \frac{4k}{5k} = \frac{4}{5} \]

Thus, the value of \( \sin A \) is \( \frac{4}{5} \).