In ΔJKL, k = 710 inches, l = 740 inches and ∠J=17°. Find the length of j, to the nearest inch. Do not approximate values until the end

In triangle \( \Delta JKL \), we are given the following:

- Side \( k = 710 \) inches (opposite angle \( K \)),
- Side \( l = 740 \) inches (opposite angle \( L \)),
- Angle \( \angle J = 17^\circ \).

We are tasked with finding the length of side \( j \) (opposite angle \( J \)) using the Law of Cosines. The Law of Cosines states:

\[
j^2 = k^2 + l^2 - 2kl \cdot \cos(\angle J)
\]

Substitute the given values:

\[
j^2 = 710^2 + 740^2 - 2(710)(740) \cdot \cos(17^\circ)
\]

Let me calculate this for you.The length of side \( j \) is approximately 216 inches.

Would you like more details or have any questions? Here are 5 related questions to expand on this problem:

1. How does the Law of Cosines relate to the Pythagorean theorem in right triangles?
2. Can you calculate the other angles in the triangle using the Law of Sines?
3. How would you solve this if you were given two angles and one side?
4. How does changing the angle \( \angle J \) affect the length of side \( j \)?
5. What happens if \( \angle J \) is an obtuse angle?

**Tip:** Always use radians when applying trigonometric functions in most programming languages.

In ΔJKL, k = 710 inches, l = 740 inches and ∠J = 17°. Find the length of j, to the nearest inch. Do not approximate values until the end.

In this problem, we use the Law of Cosines to find the length of side j in triangle ΔJKL, where k = 710 inches, l = 740 inches, and angle ∠J = 17°. Follow this step-by-step solution to solve for j with precise trigonometric calculations. Suitable for students in Grades 10-12.

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