Trig word problem. Help me please..

fayeorwhatsoever · #1 $Old$ November 20th, 2008, 07:06 AM

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.

---
Please help...Thanks is advance!

Soroban · #2 $Old$ November 20th, 2008, 08:08 AM

Hello, fayeorwhatsoever!

We need a good sketch . . .

Quote:

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