In `Delta`DEF measure of angle E is `90^(@)`. If tanD = `4/3`, and DE = 6cm, then what is the length (in cm) of side EF?

Options

A. 10
B. 5
C. 8
D. 4

Answer

To solve the problem, we will use the properties of right-angled triangles and the definition of the tangent function.

### Step-by-Step Solution:

1. **Understanding the Triangle**:
We have a right triangle DEF where angle E is 90 degrees. We know that tan(D) = opposite/adjacent. Here, the side opposite to angle D is EF and the side adjacent to angle D is DE.

2. **Using the Tangent Ratio**:
Given that tan(D) = 4/3, we can interpret this as:
\[ \text{opposite (EF)} = 4k \quad \text{and} \quad \text{adjacent (DE)} = 3k \]
where k is a common multiplier.

3. **Finding the Value of k**:
We know that DE = 6 cm. From our earlier step, we set DE = 3k:
\[ 3k = 6 \implies k = \frac{6}{3} = 2 \]

4. **Calculating the Length of EF**:
Now that we have k, we can find EF:
\[ EF = 4k = 4 \times 2 = 8 \text{ cm} \]

5. **Conclusion**:
The length of side EF is 8 cm.

### Final Answer:
The length of side EF is **8 cm**.