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Trigonometry

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A 175-pound force and a 230-pound force are acting on the same point in directions that differ by 42°.
What is the angle that the resultant makes with
the 175-pound force?

A. 22°
B. 24°
C. 32°
D. 18°

  • Trigonometry - ,

    let the 175-lb force point in the x direction. Then the 230-lb force acts at an angle θ = 42°.

    The two forces form adjacent sides of a parallelogram, with diagonal reaching to

    (175+230cos42°,230sin42°) = (346,154)
    The angle φ of the diagonal is found using

    tan φ = 154/346, so
    φ = 24°

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