Question

a certain television is advertised as a 59 - inch tv (the diagonal length). if the width of the tv is 49 inches, how tall is the tv? round to the nearest tenth of an inch.

Explanation:

Step1: Apply Pythagorean theorem

Let the height be $h$. According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c = 59$ (diagonal) and $a = 49$ (width), and $b=h$ (height). So $h^{2}=c^{2}-a^{2}$.

Step2: Substitute values

$h^{2}=59^{2}-49^{2}=(59 + 49)(59 - 49)=(108)\times(10)=1080$.

Step3: Solve for h

$h=\sqrt{1080}\approx32.9$.

Answer:

$32.9$ inches