Question 106467
The slope of the ladder is defined as the height up the wall divided by the distance from the
bottom of the wall to the foot of the ladder. In equation form this can be written as:
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{{{Slope = height/X}}}
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where "height" is the distance up the wall and "X" is the distance from the base of the
wall to the foot of the ladder. 
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You are told that the height is 8 meters and the slope can be 9.5 or 6.3. Let's first assume
that the slope is 9.5. In that case the equation becomes:
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{{{9.5 = 8/X}}}
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Get rid of the X in the denominator by multiplying both sides of this equation by X to get:
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{{{9.5X = 8}}}
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Solve for X by dividing both sides by 9.5 to get:
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{{{X = 8/9.5 = 0.842}}} meters
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and this rounds to 0.84 meters.
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At the other extreme, the slope can be 6.3. Substitute this value into the slope equation to
get:
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{{{0.63 = 8/X}}}
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Again get rid of the X in the denominator by multiplying both sides of this equation 
by X to get:
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{{{6.3X = 8}}}
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Solve for X by dividing both sides of the equation by 6.3 to get:
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{{{X = 8/6.3 = 1.2698}}} meters 
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and this rounds to 1.27 meters.
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So the answer is that the bottom of the ladder must be 0.84 meters to 1.27 meters from
the base of the wall.
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Hope this helps you to see how to do the problem.
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