To find the height of the screen, we can use the Pythagorean theorem which states that in a right triangle, the square of the length of the hypotenuse (diagonal, c) is equal to the sum of the squares of the lengths of the other two sides (legs, a and b).
For Screen A:
Let a = width = 13 inches
Let c = diagonal = 15 inches
Using the Pythagorean theorem:
c^2 = a^2 + b^2
15^2 = 13^2 + b^2
225 = 169 + b^2
b^2 = 225 - 169
b^2 = 56
b ≈ 7.5 inches (rounded to the nearest tenth)
Therefore, the approximate height of Screen A is 7.5 inches.
For Screen B:
Let a = width = 19 inches
Let c = diagonal = 22 inches
Using the Pythagorean theorem:
c^2 = a^2 + b^2
22^2 = 19^2 + b^2
484 = 361 + b^2
b^2 = 484 - 361
b^2 = 123
b ≈ 11.1 inches (rounded to the nearest tenth)
Therefore, the approximate height of Screen B is 11.1 inches.
For Screen C:
Let a = width = 28 inches
Let c = diagonal = 32 inches
Using the Pythagorean theorem:
c^2 = a^2 + b^2
32^2 = 28^2 + b^2
1024 = 784 + b^2
b^2 = 1024 - 784
b^2 = 240
b ≈ 15.5 inches (rounded to the nearest tenth)
Therefore, the approximate height of Screen C is 15.5 inches.
For Screen D:
Let a = width = 35 inches
Let c = diagonal = 40 inches
Using the Pythagorean theorem:
c^2 = a^2 + b^2
40^2 = 35^2 + b^2
1600 = 1225 + b^2
b^2 = 1600 - 1225
b^2 = 375
b ≈ 19.4 inches (rounded to the nearest tenth)
Therefore, the approximate height of Screen D is 19.4 inches.
To determine the biggest TV that will fit on the 17 x 50 inch shelf, we need to find the screen with the largest diagonal that fits within these dimensions.
Given that a diagonal of 40 inches is the largest, the biggest TV (longest diagonal) that will fit on the shelf is Screen D. Therefore, the answer is D.
Screen size: Television screens are usually measured by the diagonal of the screen. The length and width of the rectangular screen becomes the legs of our right triangle with a diagonal that is our hypotenuse. Find the height of each screen the table below, round to tenth.. Remember which is the legs and which is the diagonal or c. We want the TV to fit on a 17 x 50 inch shelf. What is the biggest TV (longest diagonal) that will fit in the shelf? Choose A, B, C, D
Screen A: Diagonal 15", Width 13"
Screen B: Diagonal 22", Width 19"
Screen C: Diagonal 32", Width 28"
Screen D: Diagonal 40", Width 35"
5 answers
whats the b stand for
Apologies for the confusion. In the given problem, "b" represents the height of the rectangular screen.
For screen A how did you get B ≈ 7.5
Apologies for the mistake in my previous response. The calculation for Screen A was incorrect.
For Screen A:
Let a = width = 13 inches
Let c = diagonal = 15 inches
Using the Pythagorean theorem:
c^2 = a^2 + b^2
15^2 = 13^2 + b^2
225 = 169 + b^2
b^2 = 225 - 169
b^2 = 56
b ≈ √56 ≈ 7.5 inches (rounded to the nearest tenth)
Therefore, the approximate height of Screen A is 7.5 inches.
For Screen A:
Let a = width = 13 inches
Let c = diagonal = 15 inches
Using the Pythagorean theorem:
c^2 = a^2 + b^2
15^2 = 13^2 + b^2
225 = 169 + b^2
b^2 = 225 - 169
b^2 = 56
b ≈ √56 ≈ 7.5 inches (rounded to the nearest tenth)
Therefore, the approximate height of Screen A is 7.5 inches.
3 answers