SOLUTION: How many feet from the base of a house must a 39-foot ladder be placed so that the top of the ladder will reach a point on the house 36-feet from the ground ? Can you Help Me With

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Question 476872: How many feet from the base of a house must a 39-foot ladder be placed so that the top of the ladder will reach a point on the house 36-feet from the ground ? Can you Help Me With That ?
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
The wall of the house forms a right angle with the ground on which the bottom of the ladder will sit. Picture that the top of the 39 foot ladder will rest on the wall of the house at a distance of 36 feet up from the bottom of the wall.
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If you can mentally picture this you can see that the ladder, wall, and the surface of the ground form a right triangle. The ladder is the hypotenuse (long side) and the height up the wall is one leg. The other leg is the distance from the base of the wall along the surface of the ground to the bottom of the ladder.
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Since this is a right triangle, the Pythagorean theorem applies. Namely the square of the hypotenuse equals the sum of the squares of the two legs. In equation form this is:
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h%5E2+=+w%5E2+%2B+b%5E2
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As indicated previously, the hypotenuse (h) is the length of the ladder which is 39 feet. Substitute this value into the equation and it becomes:
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39%5E2+=+w%5E2+%2B+b%5E2
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One of the legs (w) is the distance from the base of the wall to the point where the ladder rests against the wall. The problem tells you that this distance is 36 feet. Substitute this value into the equation for w and the equation now becomes:
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39%5E2+=+36%5E2+%2B+b%5E2
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Use a calculator to find 39 squared and 36 squared. The square of 39 is 1521 and the square of 36 is 1296. Substitute these into the equation and you now have:
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1521+=+1296+%2B+b%5E2
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Subtract 1296 from both sides of this equation and the result is:
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1521+-+1296+=+1296+-+1296+%2B+b%5E2
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Doing the subtraction reduces this equation to:
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225+=+b%5E2
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Finally solve for b by taking the square root of both sides
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sqrt%28225%29+=+sqrt%28b%5E2%29
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and you end up with:
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15+=+b
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So if you take a 39 ft ladder and place its base 15 feet from the base of the wall, when you lean the ladder against the wall, the point where the ladder rests against the wall will be 36 feet above the ground.
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Hope this helps you understand this problem a little better.