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Math Help - Trigonometry with vectors

  1. #1
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    Trigonometry with vectors

    Jack walks x km on a bearing of 100 degrees from O, then y km on a bearing of 200 degrees to H. Calculate the magnitude and direction of the displacement vector OH when:

    a) x=6, y=7
    b) x=6, y=10

    The answer to a) should be 8.4 KM, 155 degrees. And b) should be 10.7 km, 167 degrees, but I can't get these answers. Please help.
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  2. #2
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    Quote Originally Posted by tory88 View Post
    Jack walks x km on a bearing of 100 degrees from O, then y km on a bearing of 200 degrees to H. Calculate the magnitude and direction of the displacement vector OH when:

    a) x=6, y=7
    b) x=6, y=10

    The answer to a) should be 8.4 KM, 155 degrees. And b) should be 10.7 km, 167 degrees, but I can't get these answers. Please help.
    This formula:
    H_x = x \cos(100) + y \cos(200)
    H_y = x \sin(100) + y \sin(200)

    with the data given for a:
    H_x = 6 \cos(100) + 7 \cos(200)
    H_y = 6 \sin(100) + 7 \sin(200)

    magnitude =  \sqrt{ H_x^2 + H_y^2}

    direction = ArcTangent \left(\dfrac{H_y}{H_x} \right)

    When computing the arctan you need to know the quadrant:
    Quadrant 1 or 3 & Quadrant 2 or 4 and adjust the results accordingly.



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