SOLUTION: A ladder 5m long leans against a vertical wall with an angle of 70 to the ground. The ladder slips down the wall 2m down the ground. Find (a) the new angle which the ladder makes

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Question 986704: A ladder 5m long leans against a vertical wall with an angle of 70 to the ground. The ladder slips down the wall 2m down the ground. Find
(a) the new angle which the ladder makes on the ground
(b)the distance the ladder has sliped back on the ground from its original position
THANK YOU
Found 2 solutions by stanbon, Fombitz:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A ladder 5m long leans against a vertical wall with an angle of 70 to the ground. The ladder slips down the wall 2m down the ground.
Draw the picture.
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You have two overlapping right triangles.
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Original triangle measures::
base angle 70 degree
hypotenuse 5 m
height on wall 5*sin(70) = 4.7 meters
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Find
(a) the new angle which the ladder makes on the ground
New triangle measures::
hypotenuse 5 m
height on wall 4.7-2 = 2.7 meters
base angle:: sin^-1(2.7/5) = 32.68 degrees
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(b)the distance the ladder has slipped back on the ground from its original position
base = 5*cos(32.68)-5cos(70) = 2.5 meters
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Cheers,
Stan H.
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Answer by Fombitz(32388) (Show Source):
You can put this solution on YOUR website!
Find the original position of the ladder.
Distance from wall to ladder :
Distance from floor to ladder :
So the new position is,

The new position from the wall is,

So the difference in x position is,

or