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

Options

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

Answer

To solve the problem, we need to find the length of side VW in triangle UVW, where angle V is 90 degrees, tan U = 12/5, and UV = 10 cm.

### Step-by-Step Solution:

1. **Understanding the Triangle**:
In triangle UVW, angle V is the right angle. Therefore, we can label the sides as follows:
- UV is the base (adjacent to angle U).
- VW is the height (opposite to angle U).
- UW is the hypotenuse.

2. **Using the Tangent Function**:
The tangent of angle U is given by the formula:
\[ \tan U = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{VW}{UV} \]
We know that \(\tan U = \frac{12}{5}\).

3. **Substituting Known Values**:
We know that UV = 10 cm (the adjacent side). Therefore, we can substitute the values into the tangent equation:
\[ \frac{VW}{10} = \frac{12}{5} \]

4. **Cross-Multiplying**:
To find VW, we can cross-multiply:
\[ VW \cdot 5 = 12 \cdot 10 \]
This simplifies to:
\[ 5VW = 120 \]

5. **Solving for VW**:
Now, divide both sides by 5 to isolate VW:
\[ VW = \frac{120}{5} = 24 \text{ cm} \]

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

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