Answer:
48.1 inches
Step-by-step explanation:
We can use the Pythagorean theorem to find the width of the flat screen TV.
Let [tex] w [/tex] be the width of the screen. According to the Pythagorean theorem, in a right-angled triangle:
[tex] \text{hypotenuse}^2 = \text{height}^2 + \text{width}^2 [/tex]
In this case, the hypotenuse is the diagonal of the screen, which is 51 inches, and the height is 17 inches.
[tex] 51^2 = 17^2 + w^2 [/tex]
Solving for [tex] w [/tex]:
[tex] 2601 = 289 + w^2 [/tex]
[tex] w^2 = 2312 [/tex]
[tex] w = \sqrt{2312} [/tex]
Now, we know that [tex] w [/tex] is the width of the screen, so we take the positive square root:
[tex] w = \sqrt{2312} [/tex]
[tex] w = 48.08326112 [/tex]
[tex] \approx 48.1 \textsf{ inches (rounded to the nearest tenth)} [/tex]
Therefore, the width of the screen is approximately 48.1 inches (rounded to the nearest tenth).
