Question

1. canyon just bought a big screen tv. the screen has a diagonal measure of 40 inches. if the screen is 32 inches wide, how high is it?

Explanation:

Step1: Apply Pythagorean theorem

Let the height be $h$. According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c = 40$ (diagonal) and $a = 32$ (width), and $b=h$. So we have $32^{2}+h^{2}=40^{2}$.

Step2: Rearrange the equation to solve for $h$

$h^{2}=40^{2}-32^{2}$. Calculate $40^{2}=1600$ and $32^{2}=1024$. Then $h^{2}=1600 - 1024=576$.

Step3: Find the value of $h$

Take the square - root of both sides. Since $h>0$, $h=\sqrt{576}=24$.

Answer:

24 inches