A body is acted upon by forces \(F_{1} = (10 N, 090°)\) and \(F_{2} = (6 N, 180°)\). Find the magnitude of the resultant force.

To find the magnitude of the resultant force, we first need to find the horizontal and vertical components of the two given forces. For the first force, we have: - Horizontal component: $$F_{1x} = F_{1} \cos 90° = 0$$ - Vertical component: $$F_{1y} = F_{1} \sin 90° = 10 N$$ For the second force, we have: - Horizontal component: $$F_{2x} = F_{2} \cos 180° = -6 N$$ - Vertical component: $$F_{2y} = F_{2} \sin 180° = 0$$ The horizontal and vertical components of the resultant force can be found by adding the corresponding components of the two given forces: - Horizontal component: $$F_{x} = F_{1x} + F_{2x} = 0 - 6 N = -6 N$$ - Vertical component: $$F_{y} = F_{1y} + F_{2y} = 10 N + 0 = 10 N$$ The magnitude of the resultant force can be found using the Pythagorean theorem: $$|F| = \sqrt{F_{x}^{2} + F_{y}^{2}} = \sqrt{(-6)^{2} + (10)^{2}} \approx 11.66 N$$ Therefore, the magnitude of the resultant force is approximately 11.7 N. The answer is (B) 11.7 N.