Task 1 (10 pts): Determine the missing measurements for each TV. You are looking for the width, height, or diagonal. You must show all your work and fill in the table. Remember, TVs are given their size by the diagonal length. (32” means 32 inches)
32” TV height: 16” width: _____
_____ TV height: 34” width: 61”
60” TV height: 30” width: _____
_____ TV height: 20” width: 35”
52” TV height: _____ width: 45”
32” TV height: 16” width: _____
To determine the missing width, we can use the Pythagorean theorem, which states that the square of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides (height and width). We can set up the equation as follows:
16^2 + width^2 = 32^2
Simplifying the equation, we get:
256 + width^2 = 1024
Subtracting 256 from both sides, we get:
width^2 = 768
Taking the square root of both sides, we get:
width = √768 ≈ 27.7 inches
So, the missing width for the 32” TV is approximately 27.7 inches.
_____ TV height: 34” width: 61”
Since there are no missing measurements, we can leave this as it is.
60” TV height: 30” width: _____
To determine the missing width, we can again use the Pythagorean theorem. The equation can be set up as follows:
30^2 + width^2 = 60^2
Simplifying the equation, we get:
900 + width^2 = 3600
Subtracting 900 from both sides, we get:
width^2 = 2700
Taking the square root of both sides, we get:
width = √2700 ≈ 52.0 inches
So, the missing width for the 60” TV is approximately 52.0 inches.
_____ TV height: 20” width: 35”
Since there are no missing measurements, we can leave this as it is.
52” TV height: _____ width: 45”
To determine the missing height, we can once again use the Pythagorean theorem. The equation can be set up as follows:
height^2 + 45^2 = 52^2
Simplifying the equation, we get:
height^2 + 2025 = 2704
Subtracting 2025 from both sides, we get:
height^2 = 679
Taking the square root of both sides, we get:
height = √679 ≈ 26.1 inches
So, the missing height for the 52” TV is approximately 26.1 inches.