SOLUTION: An outdoor rope course consists of a cable that slopes downward from a height of 37ft to a resting place 30ft aboe the ground. The trees that the cable connects are 24ft apart. How

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Question 251544: An outdoor rope course consists of a cable that slopes downward from a height of 37ft to a resting place 30ft aboe the ground. The trees that the cable connects are 24ft apart. How long is the cable? Is the formula a^2+b^2=c^2??
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
After drawing the picture, we basically have this triangle set up:





To find the unknown length, we need to use the Pythagorean Theorem.


Remember, the Pythagorean Theorem is a%5E2%2Bb%5E2=c%5E2 where "a" and "b" are the legs of a triangle and "c" is the hypotenuse.


Since the legs are 7 and 24 this means that a=7 and b=24


Also, since the hypotenuse is x, this means that c=x.


a%5E2%2Bb%5E2=c%5E2 Start with the Pythagorean theorem.


7%5E2%2B24%5E2=x%5E2 Plug in a=7, b=24, c=x


49%2B24%5E2=x%5E2 Square 7 to get 49.


49%2B576=x%5E2 Square 24 to get 576.


625=x%5E2 Combine like terms.


x%5E2=625 Rearrange the equation.


x=sqrt%28625%29 Take the square root of both sides. Note: only the positive square root is considered (since a negative length doesn't make sense).


x=25 Simplify the square root.


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Answer:


So the solution is x=25 which means that the cable is 25 ft long.