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Math Help - Trig word problem. Help me please..

  1. #1
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    Trig word problem. Help me please..

    A magician standing on a platform subtends an angle of 15degrees at a point on the ground. The angle of elevation of the platform from the same point is 45 degrees. The magician is 180 cm high. FInd the height of the platform.


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    Please help...Thanks is advance!
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  2. #2
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    Hello, fayeorwhatsoever!

    We need a good sketch . . .


    A magician standing on a platform subtends an angle of 15 at a point on the ground.
    The angle of elevation of the platform from the same point is 45 degrees.
    The magician is 180 cm high.
    Find the height of the platform.
    Code:
                      * A
                     *|
                    * |
                   *  | 180
                  *   |
                 *    |
                *     * B
               *    * |
              *15*   |
             *  *     | h
            * *       |
           ** 45     |
        P * - - - - - * C
                h

    The magician is: AB = 180
    The height of the platform is: h = BC

    The observation point is P\!:\;\;\angle APB = 15^o,\;\angle BPC = 45^o

    Since \angle BPC = 45^o,\;\Delta BCP is an isosceles right triangle: . PC = BC = h


    In \Delta ACP\!:\;\;\tan60^o \:=\:\frac{h+180}{h} \quad\Rightarrow\quad \sqrt{3} \:=\:\frac{h+180}{h}\quad\Rightarrow\quad h \:=\:\frac{180}{\sqrt{3}-1}

    Therefore: . h \;=\;245.8845... \;\approx\;246\text{ cm}

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