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Find the angle between forces of magnitude 7N and 4N if t...

Find the angle between forces of magnitude 7N and 4N if their resultant has a magnitude of 9N.

A.

39.45°

B.

73.40°

C.

75.34°

D.

106.60°

Correct answer is B

F1=7i+0j

F2=(4cosθ)i+(4sinθ)j

9=(7+4cosθ)2+(4sinθ)2

92=(7+4cosθ)2+(4sinθ)281=49+56cosθ+16cos2θ+16sin2θ

81=49+56cosθ+16(cos2θ+sin2θ)

Recall, cos2θ+sin2θ=1

81=49+56cosθ+16814916=56cosθ

16=56cosθcosθ=1656=0.2857

\theta = \cos^{-1} 0.2857  = 73.40°