Question
Yes, Linda would like to install a new screen on the shelf that is 17 inches tall and 50 inches wide. She would like the screen to be the largest size that will fit on the shelf. She knows the diagonal and width of the 4 screens listed below. A: diagonal 15 width 13, B: diagonal 22 width 19, C: diagonal 32 width 28, D: diagonal 40 width 35. Use the Pythagorean theorem to calculate the height of each screen and complete the table.
Answers
GPT 3.5
To calculate the height of each screen using the Pythagorean theorem, we can use the formula:
h^2 = d^2 - w^2
Where h is the height, d is the diagonal and w is the width.
For screen A:
h^2 = (15^2) - (13^2)
h^2 = 225 - 169
h^2 = 56
h = √56
h ≈ 7.48
For screen B:
h^2 = (22^2) - (19^2)
h^2 = 484 - 361
h^2 = 123
h = √123
h ≈ 11.09
For screen C:
h^2 = (32^2) - (28^2)
h^2 = 1024 - 784
h^2 = 240
h = √240
h ≈ 15.49
For screen D:
h^2 = (40^2) - (35^2)
h^2 = 1600 - 1225
h^2 = 375
h = √375
h ≈ 19.36
So, the calculated heights for the screens are approximately:
A: 7.48 inches
B: 11.09 inches
C: 15.49 inches
D: 19.36 inches
h^2 = d^2 - w^2
Where h is the height, d is the diagonal and w is the width.
For screen A:
h^2 = (15^2) - (13^2)
h^2 = 225 - 169
h^2 = 56
h = √56
h ≈ 7.48
For screen B:
h^2 = (22^2) - (19^2)
h^2 = 484 - 361
h^2 = 123
h = √123
h ≈ 11.09
For screen C:
h^2 = (32^2) - (28^2)
h^2 = 1024 - 784
h^2 = 240
h = √240
h ≈ 15.49
For screen D:
h^2 = (40^2) - (35^2)
h^2 = 1600 - 1225
h^2 = 375
h = √375
h ≈ 19.36
So, the calculated heights for the screens are approximately:
A: 7.48 inches
B: 11.09 inches
C: 15.49 inches
D: 19.36 inches