Ray_Z Posted March 29, 2013 Share Posted March 29, 2013 We have satellite radio in the cars and listen to the old radio mystery programs. Sometimes they even have commercials from the era on the shows too. One of the old commercials was advertising the "new" RCA television with a 16" screen. Well, I got to thinking screen size is measured diagonally, so what is the size of the two equal sides of the screen?. Using the limited trig knowledge I have I need to have the angle opposite and the length of two of the three sides. well, I only have a given 90 degree angle and the hypotenuse [16"]. Through trial and error I found that the length of the two equal sides is about 11.375. But that's not what trig is about. Somebody come up with an equation for a triangle that has a 90 degree angle opposite and a given hypotenuse of 16". Link to comment Share on other sites More sharing options...
Steve RA Posted March 29, 2013 Share Posted March 29, 2013 How do you know it isn't a round screen. I remember the first TV our family had, back in about 47 or so, had a round screen. Link to comment Share on other sites More sharing options...
Davidoff Posted March 30, 2013 Share Posted March 30, 2013 Pythagorean theorem: a^2 + b^2 = c^2. If the sides are equal, then it reduces to 2a^2 = c^2 Thus; a = c / sqrt(2) For a 16" hypotenuse you would get a = 16"/sqrt(2) = 11.3137" In reality though, old tv's usually had an aspect ratio of 4:3, so you'd get a different result. Link to comment Share on other sites More sharing options...
MarkCO Posted March 30, 2013 Share Posted March 30, 2013 Old TVs measured straight across the middle, so the actual size was about 12" tall by 16" wide. Davidoff has the right answer for the trig question, Link to comment Share on other sites More sharing options...
Ray S Posted March 30, 2013 Share Posted March 30, 2013 Since your other two angle must add to 90 16*sin(45)=11.31 or 16*cos(45)=11.31 Link to comment Share on other sites More sharing options...
Chills1994 Posted March 30, 2013 Share Posted March 30, 2013 The diagonal of a square is always 1.414 times times the length of a side. 1.414 just so happens to be the square root of two. Another FYI... Say you have a 6/12 hip roof. All the common rafters are 6 inch rise in 12 inches of run. The gauges or buttons go on the rafter square at 6, then the other button or gauge goes on at 12. The hip rafter has the rafter square with a button at 6, the other button is put at 17. The diagonal for a 12/12 square is 17. So that's where you get the 17 inch run for the hip rafter layout. The more you know... Link to comment Share on other sites More sharing options...
Chills1994 Posted March 30, 2013 Share Posted March 30, 2013 Pythagorean theorem: a^2 + b^2 = c^2. If the sides are equal, then it reduces to 2a^2 = c^2 Thus; a = c / sqrt(2) For a 16" hypotenuse you would get a = 16"/sqrt(2) = 11.3137" In reality though, old tv's usually had an aspect ratio of 4:3, so you'd get a different result. If the ratio was 4:3, then I think the proportions shake out where the hypotenuse would be a 5, i.e. The three, four, five family of right triangles, and their multiples: 6, 8, 10 12, 16, 20 30, 40, 50 That is how you square something...a building footing/foundation ... Up. Swinging a a 3 foot arc, then a 4 foot arc, and where 5 foot swings or intersects between the first two points makes a right triangle. Link to comment Share on other sites More sharing options...
Mechanic_X Posted March 30, 2013 Share Posted March 30, 2013 (edited) already posted Edited March 30, 2013 by Mechanic_X Link to comment Share on other sites More sharing options...
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