Question

a circular window with a diameter of 26 inches is being installed over a door. the wall with the dor and window is 18 feet high. the door is 80inches from the floor to the top of the dooor. what is the distance from the cieling to the top of the window?

Answer 1

24 inches

Explanation:

First, we need to convert the height of the wall to inches since the diameter of the window is given in inches:

18 feet = 18 x 12 inches = 216 inches

Next, we can find the distance from the floor to the top of the window by subtracting the height of the door from the height of the wall and then dividing by 2 (since the window will be centered above the door):

Distance from floor to top of window = (216 inches - 80 inches) / 2 = 68 inches

Finally, we can use the Pythagorean theorem to find the distance from the ceiling to the top of the window. We can consider the triangle formed by the height of the wall, the distance from the floor to the top of the door, and the distance from the floor to the top of the window. We can let x be the distance from the floor to the top of the window, then we have:

x^2 + 80^2 = 216^2

Simplifying this equation, we get:

x² = 216² - 80²

x² = 43,296 - 6,400

x² = 36,896

x =
`√(36,896)` = 192 inches

Therefore, the distance from the ceiling to the top of the window is:

Distance from ceiling to top of window = 216 inches - 192 inches = 24 inches

So the distance from the ceiling to the top of the window is 24 inches.