Math

My Question is :

A plane with an air pf 192 miles per hour is headed on a bearing of 121 degrees. A north wind is blowing ( from north to south ) at 15.9 miles per hour. Find the ground speed and the actual bearing of the plane.

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  1. heading 121 - 90 = 31 degrees south of east
    South speed = 192 sin 31 + 15.9 = 114.8
    East speed = 192 cos 31 = 164.5
    tan of angle S of E = 114.8/164.5 = .6979
    angle S of E = 34.9
    so course made good is 90+34.9 =124.9 degrees

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  2. V = 192[121o] + 15.9[180o]. mi/h.
    X = 192*sin121 + 15.9*sin180 = 164.6. mi/h.
    Y = 192*Cos121 + 15.9*Cos180 = -114.8 mi/h.

    V = 164.6 - 114.8i = 200.7mi/h[-55.1o] = 200.7mi/h[55.1o] S. of E. = 200.7mi/h[145.1o] CW.
    Tan A = X/Y

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