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# Trig Brain Teaser

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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".

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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.

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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.

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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,

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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...

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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.

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