One of the authors of this text purchased a rear-projection Toshiba 51 H 84 television. A televi

step 1 Rectangular TVs are sized according to the lengths of their diagonals. The diagram shows a 51 in

One of the authors of this text purchased a rear-projection...

One of the authors of this text purchased a rear-projection Toshiba $51 \mathrm{H} 84$ television. A television set is "sized" according to the diagonal measurement of the viewing screen. The author purchased a $51-\mathrm{in} . \mathrm{TV},$ so the TV measures $51 \mathrm{in}$ from one corner of the viewing screen diagonally to the other corner. The viewing screen is 44.5 in. wide. Find the height of the viewing screen. (IMAGE CANT COPY)

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Key Concepts

Pythagorean Theorem

This theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. It is used to calculate the unknown side when two side lengths are known, which is crucial in problems involving measurements of rectangular screens where the diagonal forms the hypotenuse.

Right Triangle

A right triangle is a triangle in which one of the angles is exactly 90 degrees. In the context of rectangular screens, the width and height form the two shorter sides of the triangle, while the diagonal forms the hypotenuse. This relationship allows the use of the Pythagorean theorem for finding unknown dimensions.

Rectangle Geometry

In a rectangle, the diagonal creates two congruent right triangles. Understanding the geometric properties of rectangles, including the constant relationship between width, height, and diagonal, is essential for solving problems that require determining one dimension when the diagonal and another dimension are given.

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