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Math Help - finding the height of the cliff

  1. #1
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    finding the height of the cliff

    From the top of the cliff an observer spots two ships out at sea. One is north east with an angle of depression of 6 while the other is south east with an angle of depression of 4 . If the two ships are 200m apart, find the height of the cliff, to the nearest metre.

    by a long method of calculaions i got 350.92 = 351m.
    is this correct??
    is there an easier way to do it??
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  2. #2
    Member eXist's Avatar
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    If we call the height of the light house x, then the distance from ground level to each of the boats is:

    xtan(86) and xtan(84)

    However we know the angel between the boats is 90 degrees since one is NE and one is SE. So we can apply the Pythagorean theorem:

     (xtan(86))^2 + (xtan(84))^2 = 200^2

    Solve for x, should be the height of the light house.

    See this picture: (By the way, in the water view, the bottom line isn't necessarily a full line. Check the top view for a clearer view)

    Last edited by eXist; September 1st 2009 at 11:06 PM.
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  3. #3
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    ok
    so should i get to

    h^2 = (200^2) / (tan^2(86) + tan^2(84))

    then just type in calculator and get
    135.58m
    = 136m
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  4. #4
    Member eXist's Avatar
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    Correct.
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  5. #5
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    ok awesome
    thanks heaps
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  6. #6
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    do i need to take the sqrt of that???
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