`Delta DEF` is right angled at E. If `tanD = 4//3`, then what is the value of `tanF` ?

Options

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

Answer

To solve the problem, we need to find the value of \( \tan F \) in triangle \( DEF \) where \( \angle E \) is the right angle and \( \tan D = \frac{4}{3} \).

### Step-by-Step Solution:

1. **Understanding the Triangle**:
- We have triangle \( DEF \) with a right angle at \( E \).
- We denote the sides as follows:
- \( EF \) is the side opposite to angle \( D \) (perpendicular).
- \( ED \) is the side adjacent to angle \( D \) (base).

2. **Using the Tangent Definition**:
- We know that \( \tan D = \frac{\text{opposite}}{\text{adjacent}} = \frac{EF}{ED} \).
- Given \( \tan D = \frac{4}{3} \), we can set:
- \( EF = 4k \) (opposite side)
- \( ED = 3k \) (adjacent side)
- Here, \( k \) is a common multiplier.

3. **Finding the Lengths**:
- From our definitions, we have:
- \( EF = 4k \)
- \( ED = 3k \)

4. **Finding \( \tan F \)**:
- Now we need to find \( \tan F \).
- For angle \( F \), we can use the tangent definition again:
- \( \tan F = \frac{\text{opposite}}{\text{adjacent}} = \frac{ED}{EF} \).
- Substituting the values we found:
- \( \tan F = \frac{ED}{EF} = \frac{3k}{4k} = \frac{3}{4} \).

5. **Conclusion**:
- Therefore, the value of \( \tan F \) is \( \frac{3}{4} \).

### Final Answer:
\[ \tan F = \frac{3}{4} \]