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Math Help - Applied trig problem

  1. #1
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    Applied trig problem

    Hey need an explanation of how to go about this problem:

    An aircraft is sighted due west from a radar station at an elevation of 50 degrees at a height of 8000m and later at an elevation of 39 degrees and a height of 6000m on a bearing of 160 degrees. if it is descending uniformly find the angle of descent and the speed of the aircraft in km/h given that the time between the two observations is 1 minute.

    i never knew whether to put this in the pre calculus section or trig section i hope i chose the right one.

    thanks.
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  2. #2
    MHF Contributor
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    West Malaysia
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    Quote Originally Posted by clayson View Post
    Hey need an explanation of how to go about this problem:

    An aircraft is sighted due west from a radar station at an elevation of 50 degrees at a height of 8000m and later at an elevation of 39 degrees and a height of 6000m on a bearing of 160 degrees. if it is descending uniformly find the angle of descent and the speed of the aircraft in km/h given that the time between the two observations is 1 minute.

    i never knew whether to put this in the pre calculus section or trig section i hope i chose the right one.

    thanks.
    HI

    I have attached a diagram , a terrible one .. sorry bout that .

    The positions of the aircraft are A and E for the first and second observations respectively . By finding AE , then you can find its speed .

    Note that \angle COD is 110^o .

    \tan 50 =\frac{8000}{CO}\Rightarrow CO=\frac{8000}{\tan 50}

    Similarly , DO=\frac{6000}{\tan 39}

    Now , use the cosine rule ,

    CD^2=(\frac{8000}{\tan 50})^2+(\frac{6000}{\tan 39})^2-2(\frac{8000}{\tan 50})(\frac{6000}{\tan 39})\cos 110

    CD\approx 11575m

    Then CD//BE so CD=BE=11575

    AB=8000-6000=2000

    Phythagoras theorem , AE\approx 11747m

    Using s=vt , 11747=v(60) , v=196m/s

    Convert this to km/h

    You have got most of the information here , surely you can get the angle of descent .
    Attached Thumbnails Attached Thumbnails Applied trig problem-trigo-diagram.bmp  
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