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 find the width, we can use the Pythagorean theorem since we have the diagonal and the height. The formula is c^2 = a^2 + b^2, where c is the diagonal, a is the height, and b is the width.
So, substituting the given values:
32^2 = 16^2 + b^2
1024 = 256 + b^2
Subtracting 256 from both sides:
768 = b^2
Taking the square root of both sides:
b = √768
b ≈ 27.71
So, the width of the 32” TV is approximately 27.71 inches.
_____ TV height: 34” width: 61”
Since we have both the height and width measurements, there is no need to calculate anything.
60” TV height: 30” width: _____
Using the same Pythagorean theorem as before, we can find the missing width:
60^2 = 30^2 + b^2
3600 = 900 + b^2
Subtracting 900 from both sides:
2700 = b^2
Taking the square root of both sides:
b = √2700
b ≈ 51.96
So, the width of the 60” TV is approximately 51.96 inches.
_____ TV height: 20” width: 35”
Again, since we have both the height and width measurements, there is no need to calculate anything.
52” TV height: _____ width: 45”
Using the Pythagorean theorem:
52^2 = a^2 + 45^2
2704 = a^2 + 2025
Subtracting 2025 from both sides:
679 = a^2
Taking the square root of both sides:
a = √679
a ≈ 26.07
So, the height of the 52” TV is approximately 26.07 inches.
Are you sure?
Apologies for the incorrect answer. Let's correct it:
32” TV height: 16” width: _____
Using the Pythagorean theorem:
c^2 = a^2 + b^2
32^2 = 16^2 + b^2
1024 = 256 + b^2
Subtracting 256 from both sides:
768 = b^2
Taking the square root of both sides:
b = √768
b ≈ 27.71
So, the width of the 32” TV is approximately 27.71 inches.
_____ TV height: 34” width: 61”
Since we have both the height and width measurements, there is no need to calculate anything.
60” TV height: 30” width: _____
Using the same Pythagorean theorem:
c^2 = a^2 + b^2
60^2 = 30^2 + b^2
3600 = 900 + b^2
Subtracting 900 from both sides:
2700 = b^2
Taking the square root of both sides:
b = √2700
b ≈ 51.96
So, the width of the 60” TV is approximately 51.96 inches.
_____ TV height: 20” width: 35”
Since we have both the height and width measurements, there is no need to calculate anything.
52” TV height: _____ width: 45”
Using the Pythagorean theorem:
c^2 = a^2 + b^2
52^2 = a^2 + 45^2
2704 = a^2 + 2025
Subtracting 2025 from both sides:
679 = a^2
Taking the square root of both sides:
a = √679
a ≈ 26.07
So, the height of the 52” TV is approximately 26.07 inches.
what about
_____ TV height: 34” width: 61”
And
_____ TV height: 20” width: 35”
Apologies for the oversight. Let's calculate the missing measurements:
_____ TV height: 34” width: 61”
Since we have both the height and width measurements, there is no need to calculate anything.
_____ TV height: 20” width: 35”
Again, since we have both the height and width measurements, there is no need to calculate anything.
I apologize for the confusion in my previous responses.
Im sorry but you do have to calculate the tv....
Apologies for the confusion. Let's calculate the missing measurements:
_____ TV height: 34” width: 61”
Using the Pythagorean theorem:
c^2 = a^2 + b^2
c^2 = 34^2 + 61^2
c^2 = 1156 + 3721
c^2 = 4877
Taking the square root of both sides:
c = √4877
c ≈ 69.89
So, the diagonal of the TV is approximately 69.89 inches.
To calculate the missing width using the height and diagonal:
Using the Pythagorean theorem:
c^2 = a^2 + b^2
69.89^2 = 34^2 + b^2
4877 = 1156 + b^2
Subtracting 1156 from both sides:
3721 = b^2
Taking the square root of both sides:
b = √3721
b = 61
So, the width of the TV is 61 inches.
_____ TV height: 20” width: 35”
To calculate the diagonal using the height and width:
Using the Pythagorean theorem:
c^2 = a^2 + b^2
c^2 = 20^2 + 35^2
c^2 = 400 + 1225
c^2 = 1625
Taking the square root of both sides:
c = √1625
c ≈ 40.31
So, the diagonal of the TV is approximately 40.31 inches.
I apologize for the earlier confusion and appreciate your understanding.
Ok so is this right?
Yes, based on the calculations provided for the missing measurements, the answers are:
- _____ TV height: 34” width: 61”
The diagonal of the TV is approximately 69.89 inches and the width is 61 inches.
- _____ TV height: 20” width: 35”
The diagonal of the TV is approximately 40.31 inches.
These calculations should provide the correct missing measurements for the given TVs.