Hello guys, me and my friends are desperate.. We can't solve this, any ideas? Thanks!
First, it's 46.27, not 40.27. Second, your equations are wrong because of the order of operations. Last, make sure that the tangent function interprets its arguments as given in degrees, not radians. The correct system gives the height between 440 and 470 feet.
Hello, Imonars!
I would set it up like this:
A man stands at $\displaystyle A$ and sights the top of the pyramid $\displaystyle C$.Code:o C * * | * * | * * | * * |h * * | * β * α | B o - - - - - - o - - - - - - o D : 100 A x :
The angle of elevation is $\displaystyle \alpha = 46.27^o.$
He moves 100 feet away to point $\displaystyle B\!:\;AB = 100.$
The angle of elevation is $\displaystyle \beta = 40.3^o.$
The height of the pyramid is: $\displaystyle h = CD.$
Let $\displaystyle x = AD.$
In $\displaystyle \Delta CDA\!:\;\tan\alpha \,=\, \frac{h}{x} \quad\Rightarrow\quad x \,=\, \frac{h}{\tan\alpha}$ .[1]
In $\displaystyle \Delta CDB\!:\;\tan\beta \,=\, \frac{h}{x+100} \quad\Rightarrow\quad x \,=\,\frac{h}{\tan\beta} - 100$ .[2]
Equate [2] and [1]: .$\displaystyle \frac{h}{\tan\beta} - 100 \;=\;\frac{h}{\tan\alpha}$
Multipy by $\displaystyle \tan\alpha\tan\beta\!:\;h\tan\alpha - 100\tan\alpha\tan\beta \:=\:h\tan\beta$
. . $\displaystyle h\tan\alpha - h\tan\beta \:=\:100\tan\alpha\tan\beta$
. . $\displaystyle h(\tan\alpha - \tan\beta) \:=\:100\tan\alpha\tan\beta$
. . . . . . . . . . . . $\displaystyle h \:=\:\frac{100\tan\alpha\tan\beta}{\tan\alpha - \tan\beta}$
Therefore: .$\displaystyle h \;=\;\frac{100\tan46.27^o\tan40.3^o}{\tan46.27^o - \tan40.3^o} \;=\; 449.364461\hdots$