The size of a computer monitor is usually given by the length of its diagonal. A monitor's aspect ratio is the ratio of its width to its height. This monitor has a diagonal length of 27 inches and an aspect ratio of 16:9. Using ratios and the Pythagorean Theorem the approximate width is 23.5 inches and the height is _____ inches.
Well, if the aspect ratio is 16:9, we can play around with some math and humor to find the missing height. Let me put on my clown hat and get started!
First, let's assume the height is represented by 'x' inches. We can use the Pythagorean Theorem in a roundabout way to find 'x.' The theorem states that the square of the hypotenuse (the diagonal) is equal to the sum of the squares of the other two sides (width and height).
So, we have 27^2 = 23.5^2 + x^2. Now, let me reach into my imaginary bag of jokes to distract you while I calculate that for you.
After some quick calculations and a flower squirted in my face, I found that x is approximately 13.1 inches. Ta-da!
So, the height of the monitor is about 13.1 inches. Make sure to double-check those numbers, though, because clowns aren't known for their math skills (or their seriousness).
Hope that helps, and remember: laughter is the best algorithm!
To find the height of the monitor, we can use the Pythagorean Theorem.
Let's denote the width of the monitor as 'w' and the height of the monitor as 'h'. We know that the aspect ratio of the monitor is 16:9, which means the ratio of width to height is 16/9.
Using this ratio, we can write the equation:
w/h = 16/9
Cross-multiplying, we get:
9w = 16h
Simplifying, we have:
w = (16h)/9
Now, let's consider the diagonal length of the monitor.
The Pythagorean theorem states that the square of the diagonal is equal to the sum of the squares of the width and height. Therefore, we have:
(d^2) = (w^2) + (h^2)
Substituting the given values:
(27^2) = (w^2) + (h^2)
Expanding and substituting the expression for 'w' obtained earlier:
729 = ((16h)/9)^2 + (h^2)
Cross-multiplying and simplifying, we have:
729 = (256h^2 / 81) + h^2
Multiplying through by 81:
59049 = 256h^2 + 81h^2
Combining like terms:
59049 = 337h^2
Dividing both sides by 337:
h^2 = 59049 / 337
Taking the square root of both sides:
h ≈ √(59049 / 337)
h ≈ 9.04 inches
Therefore, the approximate height of the monitor is 9.04 inches.
To find the height, we need to use the aspect ratio and the Pythagorean Theorem.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (in this case, the diagonal) is equal to the sum of the squares of the other two sides (width and height).
In this case, the aspect ratio is given as 16:9, which means that for every 16 units of width, there are 9 units of height. Let's assign variables to the width and height: let x be the width and y be the height.
Using the Pythagorean Theorem, we have:
x^2 + y^2 = 27^2
Since the aspect ratio is 16:9, we can write:
x/y = 16/9
We can substitute the value of x from the aspect ratio into the Pythagorean Theorem equation:
(16y/9)^2 + y^2 = 27^2
Expanding and simplifying the equation:
256y^2/81 + y^2 = 729
Combining like terms:
(256y^2 + 81y^2)/81 = 729
Simplifying further:
337y^2 = 729 * 81
Dividing both sides by 337:
y^2 = (729 * 81) / 337
Taking the square root of both sides to find y:
y ≈ √[(729 * 81) / 337]
Calculating the approximate value using a calculator:
y ≈ √(192249 / 337)
y ≈ √570.91196
y ≈ 23.92 inches
Therefore, the approximate height of the monitor is 23.92 inches.
h/23.5 = 9/16
The diagonal really has nothing to do with it.
or,
h^2 + 23.5^2 = 27^2
and the aspect ratio really has nothing to do with it
You get the same answer either way.