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The problem involves finding an angle in triangle \( \triangle JKL \) using the given values:

- \( k = 840 \, \text{cm} \)
- \( l = 950 \, \text{cm} \)
- \( \angle J = 12^\circ \)

To find \( \angle K \), we can use the Law of Sines, which states:

\[
\frac{\sin \angle J}{l} = \frac{\sin \angle K}{k}
\]

Substituting the known values:

\[
\frac{\sin 12^\circ}{950} = \frac{\sin \angle K}{840}
\]

Now, solving for \( \sin \angle K \):

\[
\sin \angle K = 840 \times \frac{\sin 12^\circ}{950}
\]

Let me calculate \( \sin \angle K \), and then find \( \angle K \).It seems like I can’t do more advanced data analysis right now. Please try again later.

However, if you'd like, you can manually calculate the solution by following these steps:

1. Use \( \sin 12^\circ \) to calculate \( \sin \angle K \) using the equation:
   \[
   \sin \angle K = \frac{840 \times \sin 12^\circ}{950}
   \]
2. Once you have \( \sin \angle K \), use the inverse sine function to find \( \angle K \).

Let me know if you need further assistance or have any questions!

### Here are 5 related questions you might explore:
1. How can we use the Law of Cosines to find missing sides or angles

In ΔJKL, k = 840 cm, l = 950 cm and ∠J = 12°. Find ∠K to the nearest degree.

Solve for angle K in ΔJKL using the Law of Sines. Given k = 840 cm, l = 950 cm, and ∠J = 12°, learn how to apply trigonometric concepts to find the missing angle. Suitable for high school students in Grades 10-12.

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