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Chapter 7.5 Puzzle

### This assignment is due 48 hours after the Chapter Test is given.

• Puzzle solutions are due by 5:00 PM two days after the Chapter Test.
• Puzzles are worth 10 points of extra credit each.
• Answers must be accompanied by valid reasoning. Just like the tests, the answer alone isn't enough!

"Where to Sit at the Movies"

You may have debated this question with a friend, "Where shall we sit in the movie theater?" Many people do have their opinions on where the best seat in the house is located. This puzzling question can be answered using Calculus (see Stewart, p. 478).

A movie theater has a screen that is positioned 10 feet off the floor and is 25 feet high. The first row of seats is placed 9 feet from the screen and the rows are 3 feet apart. The floor of the seating area is inclined at an angle of above the horizontal and the distance up the incline that you sit is x. The theater has 21 rows of seats.

Suppose you decide that the best place to sit is in the row where the angle subtended by the screen at your eyes is a maximum. Let's also suppose that your eyes are 4 feet above the floor.

Show that:

Use a graph of as a function of x to estimate the value of x that maximizes .

In which row should you sit? What is the viewing angle in this row?

Use MAPLE to differentiate and find a numerical value for the root of the equation . Does this value confirm your results?