SOLUTION: hi somebody please help me................................. i am in desperate need of help the answer follows down for your convenience. For safetey reasons ,an extension la

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Question 106467: hi somebody please help me.................................
i am in desperate need of help
the answer follows down for your convenience.

For safetey reasons ,an extension ladder should have a slope of between 6.3 and 9.5 when it is placed against the wall.If the ladder reaches 8 m up a wall, what are the maximum and the minimum distances from the foot of the ladder to the wall?

The answer is minimum 0.84 m and maximum 1.27 m
Found 2 solutions by bucky, Earlsdon:
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
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:
.
Slope+=+height%2FX
.
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.
.
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:
.
9.5+=+8%2FX
.
Get rid of the X in the denominator by multiplying both sides of this equation by X to get:
.
9.5X+=+8
.
Solve for X by dividing both sides by 9.5 to get:
.
X+=+8%2F9.5+=+0.842 meters
.
and this rounds to 0.84 meters.
.
At the other extreme, the slope can be 6.3. Substitute this value into the slope equation to
get:
.
0.63+=+8%2FX
.
Again get rid of the X in the denominator by multiplying both sides of this equation
by X to get:
.
6.3X+=+8
.
Solve for X by dividing both sides of the equation by 6.3 to get:
.
X+=+8%2F6.3+=+1.2698 meters
.
and this rounds to 1.27 meters.
.
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.
.
Hope this helps you to see how to do the problem.
.

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
The slope is the change in the y-direction (that's vertical) over the change in the x direction (that's horizontal).
You know the vertical, that's given as 8 meters.
The horizontal (the distance from the foot of the ladder to the wall) is what you are looking for, so call that x.
The minimum slope can be written: 8%2Fx+=+6.3 so, x%5Bmax%5D+=+8%2F6.6 = 1.27 meters.
The maximum slope can be written: 8%2Fx+=+9.5 so, x%5Bmin%5D+=+8%2F9.5 = 0.84 meters.