SOLUTION: Please help me. I am having problem with this question. 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. H

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: Please help me. I am having problem with this question. 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. H      Log On


   

Question 99520: Please help me. I am having problem with this question.
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?
Thank you
Answer by timmy1729(23) About Me  (Show Source):
You can put this solution on YOUR website!
Ahh. This is a simple application of the Pythagorean Theorem! Think of the rope that Anne is pulling on as the hypotenuse since she is standing away from the tree and the rope is attached to the top of the tree and the problem said that the rope is longer than the tree's height. Then, think of the height of the tree as a side of a right triangle.
__|\
__|_\
48|__\_60
__|___\
__|____\
____x
Let's call x the distance that Anne is from the tree. The theorem is
a%5E2+%2B+b%5E2+=+c%5E2 so in our case a+=+48 and c+=+60.
So a%5E2+=+2304 & c%5E2+=+3600.
Then 2304+%2B+x%5E2+=+3600
x%5E2+=+3600+-+2304 so x%5E2+=+1296
Then x+=+36 so Anne is standing 36ft from the tree.
Also, if you notice, 48 and 60 are multiples of 12. If you divide them by 12 you get 4 and 5. That follows special triangles with sides called Pythagorean Triples. One of them is 3,4,5. So if you can notice a right triangle as having two of those sides, you can immediately know what the third side is. But, remember always show your work to get full credit in class ;-)