Need some geometry help...

Factual Questions
1

Geometry was far and away my worst math class in high school so I need help with what is probably an easy problem.

My wife and I want to buy a new TV set for Christmas. One of us wants a 36" HDTV that is of the older 4:3 ratio (more square looking) and one of us wants the newer 16:9 ratio HDTV sets (more rectangle looking) but is 34".

If you draw these two items on paper how do they look? Will the 34" TV fit ‘inside’ the larger 36" square picture or hang outside the edges?

My problem is I don’t know how to figure the lengths of the sides of each TV. I have a ratio (4:3 or 16:9), the hypotenuse (36" or 34") and one angle (90[sup]0[/sup]) of a right triangle.

I know if I have three items for any triangle I can figure out the rest but I don’t know if my ratio can be equated to the third piece of information (i.e. another length or another angle).

Any help here or do I need to visit a TV store with a tape measure? (BTW: Dimensions given for the TV’s include the case and all I’m interested in here is the picture tube itself).

Thanks in advance!

2

The 4:3 TV will be 28.8" x 21.6", and the 16:9 TV will be 29.6" x 16.7".

3

Thanks for the reply Cabbage.

I hate to ask but I don’t suppose you could show the math behind this? I only ask because I know I’ll be asked to prove it myself…‘just cuz’ or ‘because I said so’ doesn’t fly in my house anymore than it does on this board.

Thanks again for the speedy answer!

4

Actually…there’s no need to show the math behind this except for curiosity’s sake.

The good old Pythagorean Theorem (a[sup]2[/sup]+b[sup]2[/sup]=c[sup]2[/sup]) does the trick of verification I need here.

5

Give a man a fish, and he eats for a day…
Teach a man to fish, and he watches fishing shows on his big-screen TV.

With a right triangle, a[sup]2[/sup] + b[sup]2[/sup] = c[sup]2[/sup], where c is the length of the hypotenuse, and a and b are the lengths of the sides. Use this equation with the definition of the aspect ratio; for example:

a[sup]2[/sup] + b[sup]2[/sup] = 36[sup]2[/sup]
a/b = 4/3

These are two equations with two unknowns. Substitute:

(4/3*b)[sup]2[/sup] + b[sup]2[/sup] = 36[sup]2[/sup]

Simplify:

25/9*b[sup]2[/sup] = 1296
b = 21.6

Re-substitute:

a/21.6 = 4/3
a = 28.8

Tah-dah! The second problem is left as an excersise for the reader.

6

Sure. For the 4:3 TV, you’ve got the ratio of the two legs (4:3), so from that you can get the relative size of the hypotenuse from the Pythagorean theorem: 3[sup]2[/sup] + 4[sup]2[/sup] = 5[sup]2[/sup]. So we know the overall shape of the triange–horizontal leg:vertical leg:hypotenuse = 4:3:5.

Now all we have to do is scale it up to the size we want. We know the hypotenuse is 36, so we have to scale that up from 5 to 36 (multiply the 5 by a factor of 36/5). Multiply the two legs by the same scaling factor and you’ve got it:

3 * (36/5) = 21.6

4 * (36/5) = 28.8.

Then do the same type of thing for the other TV–Find the relative size of the hypotenuse, then scale it up to the desired size.

7

Whack,

Before you run out and buy the HDTV, you should read this, an excellent article by myt friend, Avi Greengart, entitled, “Why HDTV Doesn’t Matter.”

Might save yourself a few bucks.

:slight_smile: