You can
put this solution on YOUR website!It may help you to make a sketch of this problem as you work your way through the description
and analysis below. Draw a vertical line to represent the wall, a horizontal line to
show the floor, and a tilted line to represent the ladder leaning against the wall. Don't
spend a lot of time on the sketch ... just zip, zip, zip the three lines in place.
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This problem involves a right triangle. The base of the ladder rests on the floor, and the wall
is perpendicular to the wall that the ladder leans on. Where the floor and the wall meet
a right angle forms. The right triangle is formed by the floor, the wall, and the leaning
ladder. Specifically, one leg of the triangle consists of the distance the base of the ladder
is from the point where the wall and the floor meet. The problem tells you that this distance
is 2 feet. The other leg of the triangle is the distance down the wall between the point
where the ladder rests on the wall and the point where the wall and the floor meet. The
problem tells you that this distance is 15 feet. The final dimension of the right triangle
is the length of the leaning ladder. The ladder forms the hypotenuse of the right triangle
because it is opposite the right angle in the triangle. Therefore, because the hypotenuse
is the longest dimension in a right triangle, you know that the ladder will be the longest
dimension in this problem. Note that this automatically eliminates answers B and D in
your list. Why? Because the ladder has to be longer than the 15 foot distance up the wall.
Therefore, it cannot be 13.001 or 14.112 feet.
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Since the triangle is a right triangle and since two of the three dimensions of this triangle
are known, you can use the Pythagorean theorem to solve it. The Pythagorean theorem says
that in a right triangle the sum of the squares of the legs equals the square of the hypotenuse.
In equation form this is:
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in which A and B are the dimensions of the two legs of the triangle and H is its hypotenuse.
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You know that the legs are 2 ft and 15 ft. Substitute these values into the Pythagorean
equation and you get:
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Square out the two terms on the left side. 2 squared is 2 times 2 = 4 and 15 squared is
15 times 15 = 225. Substitute these results into the equation and you have:
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Add the numbers on the left side to reduce the equation to:
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Solve the equation for H by taking the square root of both sides:
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Use your calculator to find the square root of 229 and you will get 15.13274595 ft as the
answer. To the third decimal point this rounds to 15.133 ft so answer A) is the correct
answer.
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Hope this helps you to understand the problem a little better and gives you some insight
into the Pythagorean theorem and how to apply it to right triangles.
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