Question

a certain television is advertised as a 90 - inch tv (the diagonal length). if the height of the tv is 63 inches, how wide is the tv? round to the nearest tenth of an inch.

Explanation:

Step1: Apply Pythagorean theorem

Let the width be \(w\). According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c\) is the diagonal (\(c = 90\)), \(a\) is the height (\(a=63\)), and \(b\) is the width (\(b = w\)). So \(w^{2}+63^{2}=90^{2}\).

Step2: Solve for \(w^{2}\)

\(w^{2}=90^{2}-63^{2}\). Calculate \(90^{2}=8100\) and \(63^{2}=3969\). Then \(w^{2}=8100 - 3969=4131\).

Step3: Find \(w\)

\(w=\sqrt{4131}\approx64.3\)

Answer:

\(64.3\) inches