Question

a flat screen television is advertised as being 46 inches on its diagonal. if the tv is 22 inches tall, then how wide is the screen? the screen is inches wide. round your answer to the nearest tenth as needed

Explanation:

Step1: Apply Pythagorean theorem

Let $w$ = width, $h=22$ (height), $d=46$ (diagonal). The theorem states $w^2 + h^2 = d^2$, so rearrange to solve for $w$:
$$w = \sqrt{d^2 - h^2}$$

Step2: Substitute given values

$$w = \sqrt{46^2 - 22^2}$$

Step3: Calculate squared terms

$$46^2 = 2116, \quad 22^2 = 484$$

Step4: Compute difference under root

$$w = \sqrt{2116 - 484} = \sqrt{1632}$$

Step5: Calculate square root and round

$$\sqrt{1632} \approx 40.4$$

Answer:

40.4