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Question 757949: A cathedral ceiling shown in the figure below is 8 feet high at the west wall of a room. As you go from the west wall toward the east wall, the ceiling slants upward. Three feet from the west wall, the ceiling is 10.5 feet high.
What is the slope of the ceiling?
The width of the room (the distance from the west wall to the east wall) is 17 feet. How high is the ceiling at the east wall?
You want to install a light in the ceiling as far away from the west wall as possible. You intend to change the bulb, when required, by standing near the top of your stepladder. If you stand on the highest safe step of your stepladder, you can reach 21 feet high. How far from the west wall should you install the light?
I obviously need to find slope first , i tried using 10.5 as my run and 8 as my rise and a combination of others, if you can just help me find slope i think i can get the rest.
Answer by Cromlix(4381)   (Show Source):
You can put this solution on YOUR website! An intriguing problem.
The slope of the ceiling.
As the wall is 8ft high at the West wall
then if 3ft from the West wall the ceiling has risen by
2.5 ft (10.5 - 8) then using tan ratio
Tan x = 2.5/3 = 39.8 degrees
The height of the ceiling at the East wall
Distance between West and East walls = 17ft
Using the tan ratio again
Tan = Opposite/Adjacent
Tan 39.8 = Opposite/17 ft
Opposite = tan 39.8 * 17 = 14.2ft
Now you must add this to the height of the
ceiling at the West wall. So height of East wall
ceiling = 14.2 ft + 8 ft = 22.2ft.
Installing a light as far as you can from
West wall. With a limit of 21 foot stepladder.
First you must take off the 8ft for the East wall
leaving 13 ft.
Back to tan ratio.
tan 39.8 = 13/ adjacent
(Adjacent is distance from West wall)
Adjacent = 13/tan 39.8
Adjacent = 15.6ft
At 15.6 ft from the West wall you can use a 21 ft stepladder
so this is where to fix the light.
Hope this helps.
:-)
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