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4. You purchase a big-screen TV and want to install it above your fireplace. The space between your fireplace mantel and the ceiling is 42 inches. The diagonal of the TV is 40 inches. If the width of the TV is 32 inches, how tall is the TV? Is there enough space to install it above your fireplace?

Sagot :

Answers:

  • how tall is the TV?    24 inches  
  • Is there enough space to install it above your fireplace?    Yes  

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Explanation:

We have this given info:

  • The diagonal of the TV is 40 inches...the width of the TV is 32 inches

Use the pythagorean theorem to find the height of the tv.

[tex]a^2+b^2 = c^2\\\\a^2+32^2 = 40^2\\\\a^2+1024 = 1600\\\\a^2 = 1600-1024\\\\a^2 = 576\\\\a = \sqrt{576} \ \text{ note that } a > 0\\\\a = 24[/tex]

The height of the tv is 24 inches. There is enough room to install the tv above the fireplace since 24 inches is less than the 42 inches of clearance.

Let length be L

  • Breadth=B=32in
  • Diagonal=D=40in

Use Pythagorean theorem

  • L²=D²-B²
  • L²=40²-32²
  • L²=1600-1124
  • L²=576
  • L=24

As 24 is about half of 42 you can easily install the TV

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