SOLUTION: 1. A bell rope, passing through the ceiling above, just barely reaches the belfry floor. When one pulls the rope to the wall, keeping the rope taut, it reaches a point that is thre
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Question 147781: 1. A bell rope, passing through the ceiling above, just barely reaches the belfry floor. When one pulls the rope to the wall, keeping the rope taut, it reaches a point that is three inches above the floor. It is four feet from the wall to the rope when the rope is hanging freely. How high is the ceiling?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
First draw a straight line from the top of the tower to the floor. Denote the length as "x":
Now pull back the rope, this will angle the rope
Draw a triangle between the endpoint of the drawn rope to the rope's resting position. Since the horizontal length between the resting position and the new position is 4 feet (48 inches) be sure to draw that in:
Now draw a rectangle right underneath the triangle like this. Take note that the height of this rectangle is 3 inches. Also, notice how the vertical leg of the triangle is inches (subtract the height 3 from the rope length x to get inches):
So we now have a triangle. We can use Pythagorean's Theorem to find the length of the rope (which is the hypotenuse)
Start with Pythagorean's Theorem
Plug in (the length of the vertical leg), (the length of the horizontal leg), and
Square 48 to get
Foil
Subtract from both sides.
Combine like terms on the left side.
Subtract from both sides.
Combine like terms on the right side.
Divide both sides by to isolate .
Reduce.
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Answer:
So the answer is
Which approximates to
So the length of the rope (and the consequently the height of the ceiling) is 385.5 inches which is 32 1/8 feet or 32 feet 1 and a half inches.
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