Optimization Problem.

[ffuh205]

Ok here is another problem. To get the best view of the Statue of Liberty you should be at the position where ? is a maximum. If the statue stands 92 meters high, including the pedestal, which is 46 meters high, how far from the base should you be? [Hint: Find a formula for ? in terms of your distance from the base. Use this function to maximize ?, noting that 0 ? ? ? ?/2]

Ok This is what I have.

? = Tan-196/d - Tan-146/d. Solving for zero graphically ? is maximized at 66.38 meters. Plugging that back into the original equation gives us 20.6 degrees.

 

[BigGlenntheHeavy]

$\displaystyle Rewrite \ the \ correct \ problem \ verbatim \ from \ the \ book \ please, \ as \ I \ can't \ make \ heads \ or \ tails \ out$

$\displaystyle \ of \ what \ you \ have \ written.$

 

[ffuh205]

That is exactly the question.

 

[BigGlenntheHeavy]

$\displaystyle tan(\theta) \ = \ \frac{92}{d}, \ tan(\alpha) \ = \ \frac{46}{d}$

$\displaystyle \beta \ = \ \theta-\alpha, \ = \ arctan(92/d)-arctan(46/d)$

$\displaystyle \frac{d\beta}{dd} \ = \ \frac{46}{d^{2}+2116}-\frac{92}{d^{2}+8464} \ = \ 0$

$\displaystyle Hence \ d \ \dot= \ 65 \ meters, \ the \ best \ view \ to \ see \ the \ lady \ without \ the \ pedestal.$

$\displaystyle Note: \ \alpha \ \dot= \ 35.28^{0}, \beta \ \dot= \ 19.47^{0}, \ and \ \theta \ \dot= \ 54.75^{0}.$

$\displaystyle Sorry \ ffuh205, \ what \ confused \ me \ was \ your \ notation \ after \ the \ problem.$