HD Televisions are everywhere, literally. Since the phase out of the old Cathode Ray Tube (CRT) televisions, the way we watch has grown exponentially. Every way from size, 3-D, thickness, location, Wi-Fi, curved, and the number of TV’s. We are living in a time where there is no limit to the number of possibilities.
• Many of your teachers use 2 to 3 monitors for work.
• Gamers will use multiple screens if they happen to be in the same place.
• Restaurants and individuals have TVs mounted everywhere tuned into the current sporting events or news of the day. Yes I mean everywhere, even in the bathrooms.
You have two tasks for this portfolio. Be sure to show all work, save your document, and upload your document to the dropbox in Unit 6 Lesson 10 on page 2.
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”
TV Size (Diagonal) Height Width
32” 16”
34” 61”
60” 30”
20” 35”
52” 45”
Task 2 (6 pts): If a TV has the following dimensions 48” wide, 27” height, and 55” diagonal. Respond to the following questions.
▪ If the TV is 5” wider and 3” higher, what is the new diagonal measurement? (Show work)
▪ If the TV is 3” wider and 5” higher, what is the new diagonal measurement? (Show work)
▪ Depending on the previous responses, why are the diagonal measurements the same or different?
Task 1:
To determine the missing measurements for each TV, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (in this case, the diagonal of the TV) is equal to the sum of the squares of the lengths of the other two sides (height and width of the TV).
Using this formula, we can calculate the missing measurements for each TV:
1. For the 32" TV:
Height = 16"
Width = ?
Using the Pythagorean theorem:
(Width)^2 + (Height)^2 = (Diagonal)^2
(Width)^2 + (16")^2 = (32")^2
(Width)^2 + 256 in² = 1024 in²
(Width)^2 = 768 in²
Width ≈ √768 ≈ 27.7"
So the width of the 32" TV is approximately 27.7".
2. For the TV with a height of 34" and a width of 61":
Height = 34"
Width = 61"
Using the Pythagorean theorem:
(61")^2 + (34")^2 = (Diagonal)^2
3721 in² + 1156 in² = (Diagonal)^2
4877 in² = (Diagonal)^2
Diagonal ≈ √4877 ≈ 69.9"
So the diagonal of the TV is approximately 69.9".
3. For the 60" TV:
Height = 30"
Width = ?
Using the Pythagorean theorem:
(Width)^2 + (30")^2 = (60")^2
(Width)^2 + 900 in² = 3600 in²
(Width)^2 = 2700 in²
Width ≈ √2700 ≈ 52"
So the width of the 60" TV is approximately 52".
4. For the TV with a height of 20" and a width of 35":
Height = 20"
Width = 35"
Using the Pythagorean theorem:
(35")^2 + (20")^2 = (Diagonal)^2
1225 in² + 400 in² = (Diagonal)^2
1625 in² = (Diagonal)^2
Diagonal ≈ √1625 ≈ 40.3"
So the diagonal of the TV is approximately 40.3".
5. For the 52" TV:
Height = ?
Width = 45"
Using the Pythagorean theorem:
(45")^2 + (Height)^2 = (52")^2
2025 in² + (Height)^2 = 2704 in²
(Height)^2 = 2704 in² - 2025 in²
(Height)^2 = 679 in²
Height ≈ √679 ≈ 26.1"
So the height of the 52" TV is approximately 26.1".
TV Size (Diagonal) Height Width
32” 16” 27.7”
34” 61”
60” 30” 52”
20” 35” 40.3”
52” 26.1” 45”
Task 2:
1. If the TV is 5" wider and 3" higher:
Original width = 48"
New width = 48" + 5" = 53"
Original height = 27"
New height = 27" + 3" = 30"
Using the Pythagorean theorem:
(53")^2 + (30")^2 = (Diagonal)^2
2809 in² + 900 in² = (Diagonal)^2
3709 in² = (Diagonal)^2
Diagonal ≈ √3709 ≈ 60.94"
So the new diagonal measurement is approximately 60.94".
2. If the TV is 3" wider and 5" higher:
Original width = 48"
New width = 48" + 3" = 51"
Original height = 27"
New height = 27" + 5" = 32"
Using the Pythagorean theorem:
(51")^2 + (32")^2 = (Diagonal)^2
2601 in² + 1024 in² = (Diagonal)^2
3625 in² = (Diagonal)^2
Diagonal ≈ √3625 ≈ 60.21"
So the new diagonal measurement is approximately 60.21".
The diagonal measurements are different in the two scenarios because changing the width and height of a TV can affect the diagonal length, as they are all interconnected in a right triangle. The Pythagorean theorem demonstrates this relationship.