The problem is to determine how from from the base of the Statue of Liberty one should be to acheive the best view. (problem #15, section 5.6 in our Calculus book) We are told that the angle (A in the picture) from the base of the statue to it's top from your point of view on the water should be maximized in order to maximize your view of the statue.
When A is at it's maximum we also need to determine the your distance from the base of the statue (d). In order to determine where A is at a maximum we first need to come up with an equation for A, and I did this in terms of two other angles (B and C). The process I followed to finally come up with an equation for A follows.
A = B-C
tan(B) = 92/d B = arctan(92/d)
tan(A) = 46/d A = arctan(46/d)
therefore:
I could then put this equation into Maple and use the Maple program to first find the derivative of A with respect to d. If I then have Maple set this derivative equal to zero, I should come up with a local maximum, minimum or both.
Instead, I received only one solution, which was negative. Suspecting that there was another more logical positive solution based on my own calculations, I decided to graph the original equation using maple, to see if there were any other points on the graph where the slope was zero, indicating a maximum or minimum.
As you can see on this graph, the angle A actually reaches a maximum when the distance, d, from the base of The Statue of Liberty is about 65 meters. The negative answer given to us by Maple can also be true if we translate it to show that the negative indicates that if we were 65 meters on the other side of The Statue of Liberty, we would have the same view.