The length of the diagonal across the computer screen is 22 inches. If the screen measures 12 inches in height, what is the actual length of the screen to the nearest inch?
22 inches
18.43 inches
25.05 inches
32.5 inches
Let's use the Pythagorean theorem to solve for the actual length of the screen.
The Pythagorean theorem 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 (height and width):
(diagonal)^2 = (height)^2 + (width)^2
Rearranging the equation to solve for the width:
(width)^2 = (diagonal)^2 - (height)^2
(width)^2 = 22^2 - 12^2
(width)^2 = 484 - 144
(width)^2 = 340
Taking the square root of both sides:
width = √340
width ≈ 18.44 inches (rounded to the nearest hundredth)
Therefore, the actual length of the screen is approximately 18.44 inches, which is closest to 18.43 inches. So, the correct answer is 18.43 inches.
What is the missing side length of the given right triangle?
6.5 ft
3.75 ft
1.59 ft
3.9 ft
To determine the missing side length of the given right triangle, we need additional information such as the lengths of the other two sides or an angle measurement. Without this information, it is not possible to determine the missing side length.
To find the actual length of the screen, you can use the Pythagorean theorem. The diagonal of a rectangle is the hypotenuse of a right triangle formed by the height and width of the rectangle.
Let's call the width of the screen x.
According to the Pythagorean theorem:
(Height)^2 + (Width)^2 = (Diagonal)^2
12^2 + x^2 = 22^2
144 + x^2 = 484
x^2 = 484 - 144
x^2 = 340
Taking the square root of both sides:
x = √340
x ≈ 18.43 (rounded to two decimal places)
Therefore, the actual length of the screen is approximately 18.43 inches.