trigonometry math

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An aviator heads his airplane due west. He finds that because of a wind from the south, the course makes an
angle of 20" with the heading. If his airspeed is 100 mi/h, what is his groundspeed and what is the speed of the wind?

  • trigonometry math -

    Make a sketch
    His compass direction is your horizontal line with length of 100
    At the end draw a vertical line upwards, (the wind direction from the south), label it y
    draw in your hypotenuse h , his/hers actual course .
    the angle is 20°

    for speed of wind
    tan 20° = y/100
    y = 100tan20 = appr 36.4 mi/h

    for groundspeed
    cos20 = 100/h
    h = 100/cos20 = appr 106.4 mi/h

    check:
    100^2 + 36.4^2 = 11324.96
    106.4^2 = 11320.7
    close enough using my rounded answer

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