In `triangleJKL,sinL=(1)/(3),sinJ=(3)/(5), and JK=sqrt(5)` inches, the length of KL, is inches, is

Options

A. 1.7
B. `3.0`
C. 3.5
D. `4.0`

Explanation

To find the length of side KL in triangle JKL, we will use the Law of Sines. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant for all three sides of the triangle.

### Step-by-Step Solution:

1. **Identify the Given Values**:
- \( \sin L = \frac{1}{3} \)
- \( \sin J = \frac{3}{5} \)
- \( JK = \sqrt{5} \) inches

2. **Set Up the Law of Sines**:
According to the Law of Sines:
\[ \frac{\sin J}{KL} = \frac{\sin L}{JK} \]

3. **Substitute the Known Values**:
Substitute the known values into the equation:
\[ \frac{\frac{3}{5}}{KL} = \frac{\frac{1}{3}}{\sqrt{5}} \]

4. **Cross Multiply**:
Cross multiplying gives us:
\[ \frac{3}{5} \cdot \sqrt{5} = KL \cdot \frac{1}{3} \]

5. **Solve for KL**:
Rearranging the equation to isolate KL:
\[ KL = \frac{3}{5} \cdot \sqrt{5} \cdot 3 \]
\[ KL = \frac{9}{5} \cdot \sqrt{5} \]

6. **Calculate the Value**:
Now, we can calculate \( KL \):
\[ KL \approx \frac{9}{5} \cdot 2.236 \quad (\text{since } \sqrt{5} \approx 2.236) \]
\[ KL \approx \frac{9 \cdot 2.236}{5} \approx \frac{20.124}{5} \approx 4.025 \]

7. **Final Approximation**:
Rounding \( 4.025 \) gives us approximately \( 4 \) inches.

### Conclusion:
The length of KL is approximately \( 4 \) inches.

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