The size of a television screen is identified by the measurement of its diagonal. The 25-in television screen shown is 20 inches wide. What is the height of the screen?
To find the height of the television screen, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the width of the television screen (20 inches) represents one of the sides of the right triangle, and the diagonal of the screen (25 inches) represents the hypotenuse. We need to find the height of the screen, which represents the other side of the right triangle.
Using the Pythagorean theorem, we can set up the equation:
width^2 + height^2 = diagonal^2
Substituting the given values:
20^2 + height^2 = 25^2
Simplifying:
400 + height^2 = 625
To isolate the height^2 term, we subtract 400 from both sides:
height^2 = 625 - 400
height^2 = 225
To solve for height, we take the square root of both sides:
height = √225
height = 15
Therefore, the height of the television screen is 15 inches.
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) is equal to the sum of the squares of the other two sides (width and height).
Let's denote the height of the screen as "h" inches.
Now, we can set up the equation:
h^2 + 20^2 = 25^2
Simplifying, we get:
h^2 + 400 = 625
Subtracting 400 from both sides, we have:
h^2 = 225
Taking the square root of both sides, we get:
h = √225
Thus, the height of the screen is 15 inches.
20^2 + h^2 = 25^2
You should recognize this as just a multiple of the familiar 3-4-5 right triangle.