For Each Problem you must submit [upload into Bb] a running MATLAB Program [Scri

Question

For Each Problem you must submit [upload into Bb] a running MATLAB Program [Script, or the "m" file] In a text ("txt," or "doc" for instance) file provide the answers (in a table-like format, if appropriate) and comment on how you use the program to answer the questions posed in the problem. Hint: use "diary" to draft your text file with the answers. [Adapted from] Problem 4.14 [100 points] In a movie theater the "viewing angle" (theta) depends on the distance from the screen at which the viewer seats, and the dimensions of the screen as shown in the schematic below for a movie theater with the dimensions shown, find the viewing angle, theta (in degrees), for viewers seating at 45, 60, 75, and 90 ft from the screen. According to the THX specifications for movie theaters: http://myhometheater.homestead.com/Verticalviewing.html "... for most viewers physical discomfort begins when this angle exceeds 35 degrees. We strongly recommend that the layout of the auditorium adheres to this engineering guideline." Find the limiting distance to meet these specifications for the movie theater shown in the schematic.

Explanation / Answer

Here's a program. theta gives the screen viewing angle as a function of the input distance (ds) Then for part b, d(n) gives the distance and differance/lhs give the percent difference from 35 degrees %Program to find viewing angle at various distances %Set up theater specifications hs=24;%Screen height hf=6; %Screen height above floor fa=8; %floor angle %Put distance from screen here ds=[45,60,75,90]; %start by finding how high the person is from the floor h=ds*sind(8); %Now find distance to top corner of screen using distance formula dt=sqrt((hs+hf-h).^2+ds.^2); %Find distance from bottom db=sqrt((hf-h).^2+ds.^2); %Now find theta through law of cosines theta=acosd((dt.^2+db.^2-hs^2)./(2*dt.*db)) %Now find minimum viewing distance: %find cos(theta) so we don't have to worry about the cos lhs=cosd(35); err=1e6; %load error term with very large number %trial distances (we know that d

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