help with Maple please!!!!!!!!!!!!?

Question

A rectangular movie theather is 120 feet long. The top and bottom of its screen are 45 feet and 20 feet from the floor. Find the position in the theater with the largest viewing angle.

Hint: You are asked to find the position x where the angle a-b is the largest. Instead of maximizing a-b, it is easier to maximize tan (a-b).
It is easier to maximize tan (a-b). The subtraction formula for tangent will be needed. This may be found by executing expand(tan(a-b));

CAN SOMEONE PLEASE HELP ME!!!!! HOW do i solve this using maple!?!?! i dont even know how to get started!!!

here's what the situation looks like :

http://i3.tinypic.com/86pwnpk.jpg

Answer 1

Looking at the picture, we get
tan b = 20/x and tan(a+b) = 45/x.
The goal is to get y = tan a as a function of x
and then maximise this function.
To this end, note that
tan(a+b) = (tan a + tan b)/(1 - tan a tan b), so
45/x = (tan a + 20/x ) / (1 - 20/x*tan a)
= (x tan a + 20)/ (x - 20 tan a).
Clearing fractions:
45x - 900 tan a = x² tan a + 20 x
(x² + 900) tan a = 25x.
y = tan a = 25x/(x²+ 900)
with 0 <= x <= 120.
The maximum doesn't occur at either endpoint,
so we find dy/dx, set it equal to 0 and solve.
dy/dx = [25(x²+900) - 25x(2x) ]/ (x²+900)².
So x² = 900
x = 30
tan a = 750/(1800) = 5/12.
a = arctan(5/12) = 22.62 deg. (approx).
Hope that helps!

Answer 2

You've asked several math questions recently and cried for help. After people spent time working through your problems and writing down calculations, you did not even bother to rate the answers. I found this kind of impolite, and I am not going to bother answering your math questions any more.