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To find the length of \( KL \) in this triangle, we can apply the **Law of Cosines** since we have two side lengths and the included angle (angle \( K \)).

The Law of Cosines states:
\[
c^2 = a^2 + b^2 - 2ab \cdot \cos(C)
\]
where \( c \) is the side opposite the angle \( C \), and \( a \) and \( b \) are the other two sides.

In this triangle:
- \( a = 32 \) (side \( LJ \))
- \( b = 22 \) (side \( JK \))
- \( C = \angle K \)

We need to find \( \angle K \). Since we aren't given \( \angle K \) directly, please confirm if the angle values are provided elsewhere or clarify any further details. If we assume it's missing, then another method or more information would be needed to find \( KL \).

Learn how to find the length of side \( \overline{KL} \) in a triangle with given side lengths and an included angle using the Law of Cosines. This problem involves trigonometric concepts suitable for high school students.

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