2 forces with magnitude of 100 and 50 pounds act on an object at angle of 50° and 160°. Find direction and magnitude of the resultant force.?

To solve this problem, let’s assume that both angles are measured counter clockwise from the positive x axis. Each of these forces has an x and y component.

For the 100 lb force: x = 100 * cos 50, y = 100 * sin 50
For the 50 lb force: x = 50 * cos 160, y = 50 * sin 160

Total x component = 100 * cos 50 + 50 * cos 160
This is approximately 17.6 lb.

Total y = 100 * sin 50 + 50 * sin 160
This is approximately 93.7 lb.

Magnitude = √[(100 * cos 50 + 50 * cos 160)^2 + (100 * sin 50 + 50 * sin 160)^2]
This is approximately 95.3 lbs.

To determine angle counter clockwise from the positive x axis, use the following equaton.

Tan θ = y ÷ x
Tan θ = (100 * sin 50 + 50 * sin 160) ÷ (100 * cos 50 + 50 * cos 160)
θ = tan^-1 [(100 * sin 50 + 50 * sin 160) ÷ (100 * cos 50 + 50 * cos 160)]

The angle is approximately 80˚ counter clockwise from the positive x axis. I hope this is helpful for you.

angles with respect to what?
in what plane/direction is the object free to move?

If we assume the angles are measured from the positive x axis

Fx = 100cos50 + 50cos160
Fx = 17.29 lbf

Fy = 100sin50 + 50sin160
Fy = 93.71 lbf

F = √(17.29² + 93.71²)
F = 95.287...
F = 95 lbf

tanθ = Fy/Fx = 93.71 / 17.29
θ = 79.546...
θ = 80°

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Diagram ?