A force of 200N is resolve in two forces if one component is equal to 120N and makes an angle of 30¡ã with 200N force find the other force

To find the other force, we can use trigonometric principles to resolve the given force into its components.

Let's denote the force of 200N as F and the angle it makes with one of its components as θ.

First, we need to find the magnitude of the other component (the force we want to find). We know that the given component is equal to 120N, so we can subtract it from the total force:

F_other = F - 120N

Next, we need to determine the angle between the total force and the other component. Since the given component makes an angle of 30° with the total force, the angle between the total force and the other component would be 180° - 30° = 150° (since the two components are opposite directions).

Now, we can use trigonometric ratios to find the value of the other component. In this case, the cos function is suitable:

cos(150°) = adjacent / hypotenuse

cos(150°) = F_other / F

cos(150°) = F_other / 200N

Now we can rearrange the equation to solve for F_other:

F_other = cos(150°) * 200N

Using a calculator, we can calculate the value of cos(150°) as approximately -0.8660:

F_other ≈ -0.8660 * 200N

F_other ≈ -172.8N

Therefore, the other force has a magnitude of approximately 172.8N and acts in the opposite direction of the given component.