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Math Help - Base from height, and ?

  1. #1
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    Base from height, and ?

    From the top of a fire tower (100 M), two fires are seen at opposite points. (i.e., north and south) The angle of depression to one fire is 5 degrees, and 6 degrees to the other. What is the distance between the two fires (length of the base of the triangle) ?
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  2. #2
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by zoso
    From the top of a fire tower (100 M), two fires are seen at opposite points. (i.e., north and south) The angle of depression to one fire is 5 degrees, and 6 degrees to the other. What is the distance between the two fires (length of the base of the triangle) ?
    some info is missing, are the fires at ground level?
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  3. #3
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by zoso
    From the top of a fire tower (100 M), two fires are seen at opposite points. (i.e., north and south) The angle of depression to one fire is 5 degrees, and 6 degrees to the other. What is the distance between the two fires (length of the base of the triangle) ?
    assuming they are ground-level...

    Let's concentrate on the fire with 5 degree depression, if it is going down five degrees, than the amount of degrees between the distance line and the tower is 90-5=85
    so we need to find the distance between the base of the tower to the fire, to do that we use the tan of 85 and multiply by the height of the tower: 100\tan85

    Now let's concentrate on the fire with 6 degree depression, if it is going down five degrees, than the amount of degrees between the distance line and the tower is 90-6=84
    so we need to find the distance between the base of the tower to the fire, to do that we use the tan of 84 and multiply by the height of the tower: 100\tan84

    now we add the distances together...
    \boxed{100\tan85+100\tan84}

    (I don't have a calculator handy, so you'll need to find those lengths)
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  4. #4
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    Quote Originally Posted by Quick
    some info is missing, are the fires at ground level?
    Yes, the fires are at ground level. The outpost is exactly 100 M above the ground.

    The angles given are the angles between the horizontal plane that the outpost sits on, and the slopes descending to two opposite points, the fires.

    You could try and a more step by step explanation to the distance, but I think I understand anyway.
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  5. #5
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    No need, for further explanation actually, I'm pretty sure, I fully understand the processes involved.

    The final distance works out to something like 2094 m, if I'm correct
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  6. #6
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by zoso
    No need, for further explanation actually, I'm pretty sure, I fully understand the processes involved.

    The final distance works out to something like 2094 m, if I'm correct
    You are correct.
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