Two forces, f⃗ 1 and f⃗ 2, act at a point. f⃗ 1 has a magnitude of 8.80 n and is directed at an angle of 58.0 ∘ above the negative x axis in the second quadrant. f⃗ 2 has a magnitude of 6.60 n and is directed at an angle of 53.9 ∘ below the negative x axis in the third quadrant. part a what is the x component of the resultant force?

Rx  = -8.55 N :  x component of the resultant force

Explanation:

Look at the attached graphic

The given forces are shown in the graph:

F₁= 8.8N :  F₁ magnitude , α=58°    : F₁ direction

F₂=  6.6N :  F₂ magnitude , β= 53.9°    : F₂ direction

F₁ component x

F₁x = -F₁cos α = -8.8N*cos58°

F₁x : -4.66N

F₂ component x

F₂x= -F₂*cos  β = - 6.6N*cos53.9°  

F₂x= - 3.89 N

x component of the resultant force (Rx)

Rx = F₁x+ F₂x

Rx = -4.66N - 3.89 N

Rx  = -8.55 N

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