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Math Help - I know this is simple but...

  1. #1
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    I know this is simple but...

    Just started math class again this year, and all prior knowledge went down the drain on holidays.=P

    I know this is simple but...-img_20130310_100035.jpg

    P.S. Glad to have joined MHF Community. =)
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  2. #2
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    Re: I know this is simple but...

    Hello, Jaydenaus!

    A person on a boat 2 meters above sea level, has an angle of elevation of 16o to the top of a lighthouse.
    After moving 50 meters directly away from the lighthouse, the angle of elevation is 12o.
    Find the height of the top of the lighthouse above sea level.
    Code:
                                  *A
                               ** |
                            * *   |
                         *  *     |
                      *   *       |h
                   *    *         |
                *     *           |
             * 12o  * 16o          |
         D* - - - * - - - - - - - *B
         2|  50   C       x       |2
         F* - - - - - - - - - - - *E
    The height of the lighthouse above sea level is AE = h+2.
    \angle ACB = 16^o,\;\angle ADB = 12^o,\;BC = x,\;CD = 50

    In \Delta ABC\!:\;\tan16^o = \frac{h}{x} \quad\Rightarrow\quad x = \frac{h}{\tan16^o}\;\;[1]
    In \Delta ADB\!:\;\tan12^o = \frac{h}{x+50} \quad\Rightarrow\quad x = \frac{h}{\tan16^o} - 50\;\;[2]

    Equate [2] and [1]: . \frac{h}{\tan12^o} - 50 \:=\:\frac{h}{\tan6^o}

    n . . . . . . . . . . \frac{h}{\tan12^o} - \frac{h}{\tan16^o} \:=\:50

    . . . . . . . . h\left(\frac{\tan16^o-\tan12^o}{\tan12^o\tan16^o}\right) \:=\:50

    Hence: . h \;=\;\frac{50\tan12^o\tan16^o}{\tan16^o-\tan112^o} \;=\;41.07735499 \;\approx\;41\text{ m}


    Answer: . 41 + 2 \;=\;43\text{ m}
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  3. #3
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    Re: I know this is simple but...

    Thanks a lot, answered my question completely. =)
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