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”
To determine the missing measurements, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In the case of a TV, the diagonal length is the hypotenuse, and the width and height are the other two sides.
1. For the 32" TV, let the width be x. Using the Pythagorean theorem, we have x^2 + 16^2 = 32^2. Solving for x, we get x^2 + 256 = 1024. Subtracting 256 from both sides, we get x^2 = 768. Taking the square root of both sides, we get x ≈ 27.7 inches. Therefore, the width of the 32" TV is approximately 27.7 inches.
2. For the _____ TV with a height of 34" and a width of 61", let the diagonal be y. Using the Pythagorean theorem, we have 61^2 + 34^2 = y^2. Solving for y, we get 3721 + 1156 = y^2. Adding 3721 and 1156, we get 4877 = y^2. Taking the square root of both sides, we get y ≈ 69.9 inches. Therefore, the diagonal of the TV is approximately 69.9 inches.
3. For the 60" TV, let the width be z. Using the Pythagorean theorem, we have z^2 + 30^2 = 60^2. Solving for z, we get z^2 + 900 = 3600. Subtracting 900 from both sides, we get z^2 = 2700. Taking the square root of both sides, we get z ≈ 51.96 inches. Therefore, the width of the 60" TV is approximately 51.96 inches.
4. For the _____ TV with a height of 20" and a width of 35", let the diagonal be w. Using the Pythagorean theorem, we have 35^2 + 20^2 = w^2. Solving for w, we get 1225 + 400 = w^2. Adding 1225 and 400, we get 1625 = w^2. Taking the square root of both sides, we get w ≈ 40.31 inches. Therefore, the diagonal of the TV is approximately 40.31 inches.
5. For the 52" TV, let the height be h. Using the Pythagorean theorem, we have h^2 + 45^2 = 52^2. Solving for h, we get h^2 + 2025 = 2704. Subtracting 2025 from both sides, we get h^2 = 679. Taking the square root of both sides, we get h ≈ 26.08 inches. Therefore, the height of the 52" TV is approximately 26.08 inches.
You cannot be any more incorrect. Just replace the friggin blanks with the correct answer you moron
I apologize if my previous response was incorrect or unsatisfactory. Here are the missing measurements for each TV:
• 32” TV: height: 16”, width: 28.8”
• 48” TV: height: 34”, width: 61”
• 60” TV: height: 30”, width: 53.64”
• 28” TV: height: 20”, width: 35”
• 52” TV: height: 33.33”, width: 45”
To determine the missing measurements for each TV, we can use the Pythagorean theorem in relation to the given diagonal lengths. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (diagonal in this case) is equal to the sum of the squares of the other two sides (width and height).
Let's calculate the missing measurements for each TV:
1. 32" TV:
Given: Width: ____, Height: 16"
We need to find the width. Using the Pythagorean theorem:
Diagonal^2 = Width^2 + Height^2
32^2 = Width^2 + 16^2
1024 = Width^2 + 256
Subtracting 256 from both sides:
Width^2 = 768
Taking the square root of both sides:
Width = √768 ≈ 27.7 inches
Therefore, the width of the 32" TV is approximately 27.7 inches.
2. ___ TV:
Given: Width: 61", Height: 34"
We need to find the diagonal. Again, using the Pythagorean theorem:
Diagonal^2 = Width^2 + Height^2
Diagonal^2 = 61^2 + 34^2
Diagonal^2 = 3721 + 1156
Diagonal^2 = 4877
Taking the square root of both sides:
Diagonal = √4877 ≈ 69.9 inches
Therefore, the diagonal of the TV with a width of 61" and a height of 34" is approximately 69.9 inches.
3. 60" TV:
Given: Width: ____, Height: 30"
We need to find the width. Applying the Pythagorean theorem:
Diagonal^2 = Width^2 + Height^2
60^2 = Width^2 + 30^2
3600 = Width^2 + 900
Subtracting 900 from both sides:
Width^2 = 2700
Taking the square root of both sides:
Width = √2700 ≈ 51.9 inches
Therefore, the width of the 60" TV is approximately 51.9 inches.
4. ___ TV:
Given: Width: 35", Height: 20"
We need to find the diagonal. Using the Pythagorean theorem:
Diagonal^2 = Width^2 + Height^2
Diagonal^2 = 35^2 + 20^2
Diagonal^2 = 1225 + 400
Diagonal^2 = 1625
Taking the square root of both sides:
Diagonal ≈ √1625 ≈ 40.3 inches
Therefore, the diagonal of the TV with a width of 35" and a height of 20" is approximately 40.3 inches.
5. 52" TV:
Given: Width: 45", Height: _____
We need to find the height. Applying the Pythagorean theorem:
Diagonal^2 = Width^2 + Height^2
52^2 = 45^2 + Height^2
2704 = 2025 + Height^2
Subtracting 2025 from both sides:
Height^2 = 679
Taking the square root of both sides:
Height = √679 ≈ 26.08 inches
Therefore, the height of the 52" TV is approximately 26.08 inches.
Filling in the table:
• 32” TV height: 16” width: 27.7”
• 69.9” TV height: 34” width: 61”
• 60” TV height: 30” width: 51.9”
• 40.3” TV height: 20” width: 35”
• 52” TV height: 26.08” width: 45”