Please help!!

please. Can I at least get a hint to start the first question.

Thank you
 
\(\displaystyle \theta\) was determined using the law of cosines.

"a" represents the length of the upper line of sight, "b" represents the length of the lower line of sight.
 
The referenced document contains the following textual exercise:

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 set 3 feet apart. The floor of the seating area is inclined at an angle of alpha = 20 degrees above horizontal and the distance up the incline that you sit is "x". The theater has 21 rows of seats, so 0 < x < 60.

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

Code: 
   |  *
   |        *
   |              *
   |             theta  *|
25 |              *      |4   .
   |        *             .
----  *              .
   |            .
10 |       . alpha
   -----|------------------------
      9 |
1. Show that theta = arccos[(a[sup:2uuit2bv]2[/sup:2uuit2bv] + b[sup:2uuit2bv]2[/sup:2uuit2bv] - 625) / (2ab)], where:

. . . . .a[sup:2uuit2bv]2[/sup:2uuit2bv] = [9 + x cos(alpha)][sup:2uuit2bv]2[/sup:2uuit2bv] + [31 - x sin(alpha)][sup:2uuit2bv]2[/sup:2uuit2bv]

. . . . .b[sup:2uuit2bv]2[/sup:2uuit2bv] = [9 + x cos(alpha)][sup:2uuit2bv]2[/sup:2uuit2bv] + [x sin(alpha) - 6][sup:2uuit2bv]2[/sup:2uuit2bv]

2. Use a graph of theta as a function of x to estimate the value of x that maximizes theta. In which row should you sit? What is the viewing angle theta for this row?

3. Use your computer algebra system to differentiate theta and find a numerical value for the root of the equation d(theta)/dx = 0. Does this value confirm your result in (2)?

4. Use the graph of theta to estimate the average value of theta on the interval 0 < x < 60. Then use your CAS to compute the average value. Compare the maximum and minimum values of theta.
Click to expand...
 
Thank you! I've shown all side using the law of cosine and trig ratios
 
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