In `Delta` XYZ measure of angle Y is 90°. If tanX = 15/8, and XY = 16cm, then what is the length (in cm) of side YZ?

Options

A. 34
B. 30
C. 15
D. 14

Answer

To solve the problem, we will use the properties of a right triangle and the definition of the tangent function.

### Step-by-Step Solution:

1. **Identify the Triangle and Given Information:**
- We have a right triangle \( \Delta XYZ \) where \( \angle Y = 90^\circ \).
- We are given that \( \tan X = \frac{15}{8} \) and \( XY = 16 \, \text{cm} \).

2. **Understanding the Tangent Function:**
- The tangent of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the adjacent side.
- For \( \tan X = \frac{15}{8} \):
- The opposite side to angle \( X \) is \( YZ \) (which we need to find).
- The adjacent side to angle \( X \) is \( XY \).

3. **Setting Up the Ratio:**
- From the tangent definition:
\[ \tan X = \frac{YZ}{XY} \]
- Substituting the known values:
\[ \frac{15}{8} = \frac{YZ}{16} \]

4. **Cross-Multiplying to Solve for \( YZ \):**
- Cross-multiplying gives:
\[ 15 \cdot 16 = 8 \cdot YZ \]
- Simplifying this:
\[ 240 = 8 \cdot YZ \]

5. **Dividing to Isolate \( YZ \):**
- Now, divide both sides by 8:
\[ YZ = \frac{240}{8} = 30 \, \text{cm} \]

6. **Conclusion:**
- The length of side \( YZ \) is \( 30 \, \text{cm} \).

### Final Answer:
The length of side \( YZ \) is \( 30 \, \text{cm} \).

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