The magnitude obtained when adding vector A (80 N at 20 deg) with vector B (40 N at 70 deg) is:

110.06 N

89.85 N

0 130.32 N

0 141.98 N

Explanation:

The magnitude of the force is known as the resultant.

R = √Fx²+Fy²

Fx = 80cos 20 + 40cos70

Fx = 80(0.9397)+40(0.3420)

Fx = 75.176 + 13.68

Fx = 88.856N

Fy = 80sin 20 + 40sin70

Fy = 80(0.3420)+40(0.9397)

Fy = 27.36 + 37.588

Fy = 64.948N

R = √88.586²+64.948²

R = √7,847.48+4,218.24

R = √12,065.72

R = 109.5

R = 110N

Hence the magnitude of the forces is 110N

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