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 $h$, width $w = 49$ inches and diagonal $d=59$ inches. According to the Pythagorean theorem $d^{2}=h^{2}+w^{2}$, so $h^{2}=d^{2}-w^{2}$.

Step2: Substitute values

Substitute $d = 59$ and $w = 49$ into the formula: $h^{2}=59^{2}-49^{2}=(59 + 49)(59 - 49)=(108)\times(10)=1080$.

Step3: Solve for $h$

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

Answer:

$32.9$ inches