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Math Help - Bearing/Navagation PreCal Problem

  1. #1
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    Question Bearing/Navagation PreCal Problem

    From city A to city B, a plane flies 650 miles at a bearing N48degreesE. From city B to city C the plane flies 810 miles at a bearing S36degreesE. Find the return distance from C to A and the bearing from C to A.


    I'm unsure of if I use 36 degrees as the angle measure for B. I believe 42 degrees would be angle A's measurement. If this is correct, I got 711.5293 miles from city C to A using the Law of Sines. How would I go about finding the bearing from C to A?

    Thanks!
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  2. #2
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    Quote Originally Posted by accordry View Post
    From city A to city B, a plane flies 650 miles at a bearing N48degreesE. From city B to city C the plane flies 810 miles at a bearing S36degreesE. Find the return distance from C to A and the bearing from C to A.


    I'm unsure of if I use 36 degrees as the angle measure for B. I believe 42 degrees would be angle A's measurement. If this is correct, I got 711.5293 miles from city C to A using the Law of Sines. How would I go about finding the bearing from C to A?

    Thanks!
    First thing to do is sketch the figure. In geometry it is important that you have the correct figure or diagram....especially with bearings.

    The figure would be a triangle ABC where
    AB = 650 mi
    BC = 810 mi
    angle ABC = angle B = 48 +36 = 84 degrees

    Why 48 +36?
    Because at point B, if you drop a vertical line to signify the South axis, then the bearing of BA is S 48deg W ....just the opposite of the bearing of AB, which is given as N 48deg E.

    So in the figure, there are two known sides and their included angle. So use the Law of Cosines to find the 3rd side.
    (CA)^2 = (650)^2 +(810)^2 -2(650)(810)cos(84deg)
    CA = 984.14 mi --------answer.

    Now you can get the angle C by the Law of Sines:
    650/ sinC = 984.14 /sin(84deg)
    angle C = arcsin[650*sin(84) /984.14deg)
    angle C = 41.06 deg, or, say, 41 degrees.

    Then, for the bearing of CA,
    here is one way,
    draw a North-South crossline at point C.
    it is easy to see now the bearing of CA.
    it is N (36 +41 = 77) W....or N 77deg W -------answer.
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  3. #3
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    Thanks sooo much! I actually think I understand it now.
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