Question

a flat screen television is advertised as being 43 inches on its diagonal. if the tv is 19 inches tall, then how wide is the screen? the screen is inches wide. round your answer to the nearest tenth as needed question help: message instructor check answer

Explanation:

Step1: Identify the formula (Pythagorean theorem)

The TV screen is a rectangle, so the diagonal forms a right triangle with the height and width. The Pythagorean theorem is \( a^{2}+b^{2}=c^{2} \), where \( c \) is the diagonal, \( a \) is the height, and \( b \) is the width. Here, \( c = 43 \), \( a = 19 \), and we solve for \( b \). Rearranging the formula: \( b=\sqrt{c^{2}-a^{2}} \).

Step2: Substitute the values

Substitute \( c = 43 \) and \( a = 19 \) into the formula: \( b=\sqrt{43^{2}-19^{2}} \). Calculate \( 43^{2}=1849 \) and \( 19^{2}=361 \). Then, \( 1849 - 361 = 1488 \). So, \( b=\sqrt{1488} \).

Step3: Calculate the square root

Calculate \( \sqrt{1488}\approx38.6 \) (rounded to the nearest tenth).

Answer:

38.6