A certain television is advertised as a 83-inch TV (the diagonal length). If the height of the TV is 45 inches, how wide is the TV? Round to the nearest tenth of an inch. Answer Attemptiout of5 square in.

## Step 1<br />The problem involves the application of the Pythagorean theorem, which states that in a right-angled 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. This can be written as:<br />### \(a^2 + b^2 = c^2\)<br />where \(c\) is the hypotenuse and \(a\) and \(b\) are the other two sides.<br /><br />## Step 2<br />In this problem, the hypotenuse is the diagonal of the TV, which is 83 inches. of the TV, which is one of the other sides, is 45 inches. We are asked to find the width of the TV, which is the remaining side.<br /><br />## Step 3<br />We can rearrange the Pythagorean theorem to solve for the width:<br />### \(b = \sqrt{c^2 - a^2}\)<br /><br />## Step 4<br />Substitute the given values into the formula:<br />### \(b = \sqrt{83^2 - 45^2}\)<br /><br />## Step 5<br />Calculate the square of 83 and 45, subtract the latter from the former, and then take the square root of the result.<br /><br />## Step 6<br />Round the result to the nearest tenth of an inch.