4. One night you are watching a movie with your significant other, who has 20/20

Question

4. One night you are watching a movie with your significant other, who has 20/20 vision. You know that he/she likes to read the subtitles, which are 0.25 inches in height. The TV is 43 inches wide and the subtitles start and end 1 inch from each edge of the screen. What is the maximum distance you can have the couch (its center) from the TV, while keeping all the subtitles readable for your significant other? Assumptions: His/her eyes will be the same distance away from the screen as the couch. His/her eyes (and the center of the couch) will be aligned with the middle (width) of the TV screen and be level (in height) with the subtitles. Round to two decimal places Diagram is not to scale 43.0 o2s SUBTITLES 1.0 1.0 Determine this distance

Explanation / Answer

20/20 means you can subtend 5 minutes of arc.

The greatest distance is to the edge of the subtitiles =Sqrt (d^2+(43/2-1)^2)

arc=0.25/greatest distance = 5*2pi/360/60

sqrt(d^2+20.5^2)=.171

Thus d=Sqrt(171^2-20.5^2)=169.7 inches = 4.31 m

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