Question

a certain television is advertised as a 38-inch tv (the diagonal length). if the width of the tv is 29 inches, how tall is the tv? round to the nearest tenth of an inch.

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle (TV screen is a rectangle, so diagonal forms right triangle with width and height), \(a^2 + b^2 = c^2\), where \(c\) is diagonal, \(a\) is width, \(b\) is height. Here, \(c = 38\), \(a = 29\), solve for \(b\).

Step2: Rearrange formula

\(b^2 = c^2 - a^2\). Substitute values: \(b^2 = 38^2 - 29^2\). Calculate \(38^2 = 1444\), \(29^2 = 841\). So \(b^2 = 1444 - 841 = 603\).

Step3: Solve for \(b\)

\(b = \sqrt{603} \approx 24.6\) (rounded to nearest tenth).

Answer:

\(24.6\) inches