This is a two step communicating and applying geometrical skills worksheet! Please help me solve it with an explanation! Will give five start favorite and points Please ASAP!!!!!

FIRST PAGE: The Simple Version
Where will you have the best view of the
screen in a movie theater?
In this theater, the screen is 22 feet tall,
and is 10 feet off the floor. The rows of
seats are 3 feet apart. When seated, your
eyes are 4 feet from the floor. Call the
distance between you and the screen x.
The best view is in the row where the
viewing angle is largest.
Some helpful suggestions:
1. Find an equation that relates x to the angle between the horizontal and the bottom of
your view. (You should give this angle a name.)
2. Find an equation that relates x to the angle between the horizontal and the top of your
view. (Name this one too.)
3. Find an equation that describes how the viewing angle Ө changes as x changes. (Get
Ө in terms of the other angles.)
4. Graph this last equation and find exact values where necessary.

Don’t forget: you’re trying to figure out which row to sit in.


PAGE 2: The Advanced Version USE COMMUNICATION

In most modern theaters, the floor is not flat.
Using what you learned in your investigation
of the simple version, briefly discuss why
movie theater floors are built at an angle.
Now, assume that the theater has a floor that
makes a 25o angle with the horizontal.
Everything else about the theater is the same.
Find the best row, and compute how much
greater your viewing angle is here, compared
with the best seat in the theater with the flat
floor.

More helpful suggestions:
1. Notice that in the simple version, when x changed our eyes simply moved back
horizontally. Now, the height of our eyes also changes when x changes. Look at the
triangle formed by the floor and level ground and write the coordinates of your eyes
(distance back from the front and up from level ground) in terms of x.
2. Now write expressions for the distance from your eyes to the bottom of the screen
(marked a) and eyes to the top of the screen (call it b) in terms of x.
3. Recall that when we know the lengths of 3 sides of any triangle, we can use the Law of
Cosines to find any angle. You can guess which one we care about: find Ө.
4. Don’t forget to use appropriate forms of representation to communicate your
presentation of the information.