SOLUTION: I need help solving the following word problem: Anne is pulling on a 60-foot rope attached to the top of a 48-foot tree while Walter is cutting the tree at its base. How far fr

Question 84565: I need help solving the following word problem:
Anne is pulling on a 60-foot rope attached to the top of a 48-foot tree while Walter is cutting the tree at its base. How far from the base of the tree is Anne standing?
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
The vertical tree forms a right angle with the ground. Therefore, you can suspect that this
problem is going to involve a right triangle.
.
The height of the tree will be one leg of the triangle.
.
The 60 foot long rope that Anne is pulling on will be the hypotenuse of this right triangle.
.
And the unknown distance (D) that Anne is from the base of the tree is the other leg of
the triangle.
.
You can solve this using the Pythagorean theorem which says that if you square each leg
and add the sums of these squares together, the answer will equal the square of the hypotenuse.
In equation form that is:
.

.
where L represents one of the legs and H is the hypotenuse. We know that one of the legs
is 48 feet long, the hypotenuse is 60 feet long, and the missing leg is D. Substituting
these values into the equation results in:
.

.
Squaring the 48 and the 60 changes the equation to:
.

.
get rid of the 2304 on the left side by subtracting 2304 from both sides. When you do
the problem reduces to:
.

.
You can now find D by taking the square root of both sides to get:
.

.
So Anne is standing 36 ft from the base of the tree. Do you see the problem here? The
tree is 48 feet tall and when it starts falling toward Anne, she is too close to it.
If she continues to stand 36 feet from the base of the 48 foot long tree, it's going to
give her a whack she won't forget. When it starts to topple she needs to move back more
than 12 feet or she needs to move to the side and out of the path of the falling tree.
What this problem tells you is that she should have a rope longer than 60 feet to pull on.
If you work it out, in order for Anne to be 48 feet away from the base of the 48 ft tall tree
she needs a rope that is about 68 feet long. And that's cutting it close also.
.
Hope this helps you to understand the problem a little better.
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