In `DeltaUVW` measure of angle V is `90^(@)` .If `tanU=(12)/(5), andUV=10` cm , then what is the length (in cm. of side VW ?

Options

A. 26
B. 24
C. 25
D. 5

Answer

To find the length of side VW in triangle UVW where angle V is 90 degrees, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Angle V = 90 degrees
- \( \tan U = \frac{12}{5} \)
- Length of side UV = 10 cm

2. **Understanding the Tangent Function:**
- In a right triangle, the tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side.
- Here, for angle U, the opposite side is VW and the adjacent side is UV.

3. **Set Up the Tangent Ratio:**
- From the definition of tangent:
\[ \tan U = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{VW}{UV} \]
- Substituting the known values:
\[ \frac{12}{5} = \frac{VW}{10} \]

4. **Cross-Multiply to Solve for VW:**
- Cross-multiplying gives:
\[ 12 \cdot 10 = 5 \cdot VW \]
- This simplifies to:
\[ 120 = 5 \cdot VW \]

5. **Isolate VW:**
- To find VW, divide both sides by 5:
\[ VW = \frac{120}{5} = 24 \text{ cm} \]

6. **Conclusion:**
- The length of side VW is 24 cm.

### Final Answer:
The length of side VW is **24 cm**.