Question 458282
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Let *[tex \Large \theta] be the smaller of the two angles and *[tex \Large \varphi] be the larger.  Let *[tex \Large x] be the distance from the base of the tree to the point where the first angle measurement was taken, then the point where the second angle measure was taken was at *[tex \Large x\ -\ 10] feet from the base of the tree.  Finally, let *[tex \Large y] represent the height of the tree.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \cot\theta\ =\ \frac{x}{y}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \cot\varphi\ =\ \frac{x\ -\ 10}{y}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\cot\theta\ =\ x]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\cot\varphi\ +\ 10\ =\ x]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y(\cot\varphi\ -\ \cot\theta)\ =\ -10]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ \frac{-10}{\cot\varphi\ -\ \cot\theta}]


You can do your own arithmetic.  Remember to make sure your calculator is in Degrees mode (or use the *[tex \LARGE \frac{\pi}{180}] conversion from degrees to radians).  By the way, I measured the angles with my Acme Excelsior 9000 Pro sextant -- couldn't find my Handy Dandy sextant.  Got the same answer though.  DO NOT chop down that tree.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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