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Trig Math

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I need help with this problem. I don't get how to do it or how they got that answer.
A force of 50 pounds acts on an object at an angle of 45 degrees. A second force of 75 pounds acts on the object at an angle of -30 degrees. What was the direction and the magnitude of the resultant force?

The answer is |F|≈ 100.33 lb and Ө ≈ -1.22 degress

  • Trig Math - ,

    From the origin on the x-axis draw a line at 45 degrees with length 50
    From the origin draw a line 30 degrees down into the fourth quadrant with length 75

    So the angle between the two forces is 75 degrees.
    Complete the parallelogram and draw the diagonal.
    That diagonal is the resultant force F

    I see a triangle with sides 50 and 75 and an angle of 105 degrees between them. ... (180-75)

    By Cosine Law
    |F|^2 = 50^2 + 75^2 - 2(50)(75)cos 105
    = 10066.1428
    |F| = 100.33

    Now by Sine Law
    SinØ/75 = sin 105/100.33
    sinØ = .72206
    Ø = 46.225

    so subtracting the 45 from that leaves us with Ø = 1.225 below the x-axis or -1.225 degrees

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