Television sets are sized according to the length of the diagonal of the screen. The Tuber family just purchased a 61" high-definition television. They measured the length of the screen to be sure it would fit into their space, but they forgot to measure the height. If the television is 53" wide, which is the closest, in inches, to the height of the screen?

Since televisions are usually sized according to the length of the diagonal of the screen, the size forms the hypotenuse while the width of the tv forms the adjacent of a right angle triangle according to the attached image.

In order to find the closest height of the television, the Pythagoras theorem is applied;

[tex]hypothenuse^2 = oppositte^2 + adjacent^2[/tex]

Hence,

[tex]61^2 = height^2 + 53^2[/tex]

height = √[tex]61^2-53^2[/tex]

= √912

= 30.2"

Therefore, the closest height of the screen is 30.2 inches.

shrutiagrawal1798 shrutiagrawal1798 · Answer 2 · 2021-12-17T11:58:09+01:00

The height of 61" high-definition television has been 30.2".

Since the measurement of the television have been performed with the diagonal measurement, the height of the triangle with width of the television results in the right angle triangle.

The measurement of diagonal for the right angle triangle has been given by:

[tex]\rm Diagonal^2\;=\;Height^2\;+\;Width^2[/tex]

The given television has diagonal = 61"

Width of the television = 53"

Substituting the values,

[tex]\rm 61^2\;=\;height^2\;+\;53^2[/tex]

[tex]\rm3,721\;=\;height^2\;+\;2,809[/tex]

3,721 - 2,809 = [tex]\rm \;height^2[/tex]

Height = [tex]\rm \sqrt{912}[/tex]

Height = 30.199"

Height = 30.2"

The height of 61" high-definition television has been 30.2".

For more information about the height of triangle, refer to the link:

https://brainly.com/question/2142821