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Math Help - Height of Aircraft

  1. #1
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    Height of Aircraft

    Two sensors are spaced 700 feet apart along the approach to a small airport. When an aircraft is nearing the airport, the angle of elevation from the first sensor to the aircraft is 20 degrees and from the second sensor to the aircraft it is 15 degrees. Determine how high the aircraft is at this time.
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  2. #2
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    Quote Originally Posted by magentarita View Post
    Two sensors are spaced 700 feet apart along the approach to a small airport. When an aircraft is nearing the airport, the angle of elevation from the first sensor to the aircraft is 20 degrees and from the second sensor to the aircraft it is 15 degrees. Determine how high the aircraft is at this time.
    Pardon my artwork, but this one needs a picture. See attachment.

    \tan 20=\frac{A}{X}

    X\tan20=A [1]

    \tan 15=\frac{A}{X+700}

    (X+700)\tan 15=A [2]

    X\tan20=(X+700)\tan 15

    X\tan20=X\tan15+700\tan15

    X\tan20-X\tan15=700\tan 15

    X(\tan20-\tan15)=700\tan15

    X=\frac{700\tan15}{\tan20-\tan15}

    X\approx 1953.37 ft.

    Now substitute back into one of the first equations for A.

    A=X\tan20 ft.

    A\approx710.9678247
    Attached Thumbnails Attached Thumbnails Height of Aircraft-airplane.bmp  
    Last edited by masters; November 14th 2008 at 03:39 PM.
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  3. #3
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    wonderfully done!

    Quote Originally Posted by masters View Post
    Pardon my artwork, but this one needs a picture. See attachment.

    \tan 20=\frac{A}{X}

    X\tan20=A [1]

    \tan 15=\frac{A}{X+700}

    (X+700)\tan 15=A [2]

    X\tan20=(X+700)\tan 15

    X\tan20=X\tan15+700\tan15

    X\tan20-X\tan15=700\tan 15

    X(\tan20-\tan15)=700\tan15

    X=\frac{700\tan15}{\tan20-\tan15}

    X\approx 1953.37 ft.

    Now substitute back into one of the first equations for A.

    A=X\tan20 ft.

    A\approx710.9678247
    What can I say? You did fabulous!
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