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Problem: Three forces F1, F2, and F3 are acting on a particle in equilibrium. F1 = 10 N, F2 = 15 N. The angle between F1 and F2 is 120 degrees. The angle between F2 and F3 is 135 degrees. Find F3. Steps: 1. Identify angles: Angle between F1 and F2 is 120°. Angle between F2 and F3 is 135°. The total angle around the point is 360°. So, angle between F3 and F1 is 360 - 120 - 135 = 105°. 2. Apply Lami's Theorem: F1/sin(angle opposite F1) = F2/sin(angle opposite F2) = F3/sin(angle opposite F3). Note: The angle opposite to a force is the angle between the other two forces. Angle opposite F3 is the angle between F1 and F2, which is 120°. Angle opposite F1 is the angle between F2 and F3, which is 135°. 3. Set up equation: F3 / sin(120°) = F1 / sin(135°). 4. Substitute values: F3 / sin(120°) = 10 / sin(135°). sin(120°) ≈ 0.866, sin(135°) ≈ 0.707. F3 / 0.866 = 10 / 0.707. F3 / 0.866 ≈ 14.14. F3 ≈ 14.14 * 0.866 ≈ 12.25 N. Answer: F3 is approximately 12.25 N.