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
What is the width of the TV?
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To find the width of the TV, we can use the Pythagorean theorem. The size of the TV is given as its diagonal (32 inches), and we know the height (15.7 inches). We can set this up as follows:
Let ( w ) be the width of the TV. According to the Pythagorean theorem:
[
w^2 + (15.7)^2 = (32)^2
]
Calculating ( (32)^2 ):
[
32^2 = 1024
]
Calculating ( (15.7)^2 ):
[
15.7^2 = 246.49
]
Now, plug these values into the equation:
[
w^2 + 246.49 = 1024
]
Subtract ( 246.49 ) from both sides:
[
w^2 = 1024 – 246.49
]
[
w^2 = 777.51
]
Now, take the square root of both sides to find ( w ):
[
w = sqrt{777.51} approx 27.88 text{ inches}
]
So, the width of the TV is approximately 27.88 inches.