Math Is Fun Forum

Chrish77

Guest

Trig / Geometry Problem relating to a TV's Size.

I will do my best to describe this problem.
I have a question that a friend and mine could not answer.

He was looking for a TV stand and had come unprepared. He knew he wanted to buy a 32 inch LCD at a ratio of 16:9. He wanted to know how long the base of the TV would be so he would know what size of TV stand he should buy.

We know that it’s a 32inch TV so the hypotenuse is 32 inches.
We do Not know A or B, but we know C is 90 degree angle
And we know the ratio of a is 9 and c is 16 for the 16:9 ratio of the TV.

We know the problem would look like this.

Corner to corner is c
     -----------------------------------
      |                                      |
      |                                      | a
      |                                      |
      ----------------------------------C
              b

I know that A^2 + B^2 = C^2

We tried a few different formulas but nothing worked out.

Anyone know how to solve this problem?

Thanks
Chris

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Trig / Geometry Problem relating to a TV's Size.

Put the stuff you know into the A² + B² = C² equation.
As you said, it's a 32 inch TV, and so C=32, meaning C² = 1024.

You don't know the lengths of A and B, but you do know their lengths relative to each other.
So you can replace A and B with 9x and 16x, where x is some unknown value.

Now you have (9x)² + (16x)² = (81+256)x² = 337x² = 1024.
Therefore, x² = 1024/337 and x = √(1024/337) ≈ 1.743.

Placing this value into 9x and 16x should get you the lengths A and B.

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Why did the vector cross the road?
It wanted to be normal.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Trig / Geometry Problem relating to a TV's Size.

mathsy is right! And if you like backwards tan and normal cos,
you can do 32 multiply cos[inverseTan(9/16)].
You learn about tan and cos in geometry.
They are useful for physics and engineering too.
The backwards tangent gets you the angle by
starting with two perpendicular distances.
"Deg" means "degrees" on your calculator.
Sometimes the screen says "DEG" somewhere on it.
Another funny one is "RAD" for "radians", but
that is weird and theoretical and 3.14159265-like.
Today is 3.14 pi day.

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igloo myrtilles fourmis

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Trig / Geometry Problem relating to a TV's Size.

Oh yeah, the answer:  27.89041719 inches wide.

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igloo myrtilles fourmis

Chrish77

Guest

Re: Trig / Geometry Problem relating to a TV's Size.

Hi mathsy

Thanks for the reply, we were really close to what you had, but we forgot some of the rules, haven’t used those since first year math in University lol. We got up too 9A^2+16A^2 = 32^2 but after that we messed up the math.
Anyway thank you very much for the help.

Chris