Question

the size of a tv is measured by its diagonal. you want to buy a tv that has a 32-inch screen and a height of 15.7 inches. what is the width of the tv? 16.3 inches 27.88 inches 35.64 inches 1,024 inches

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle (TV screen is a rectangle, diagonal forms right triangle), \( a^2 + b^2 = c^2 \), where \( c \) is diagonal, \( a \) is height, \( b \) is width. So \( b = \sqrt{c^2 - a^2} \).

Step2: Substitute values

\( c = 32 \), \( a = 15.7 \). Calculate \( c^2 = 32^2 = 1024 \), \( a^2 = 15.7^2 = 246.49 \). Then \( c^2 - a^2 = 1024 - 246.49 = 777.51 \).

Step3: Find square root

\( b = \sqrt{777.51} \approx 27.88 \).

Answer:

27.88 inches (corresponding to the option: 27.88 inches)