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

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) (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 where "a" and "b" are the legs of a triangle and "c" is the hypotenuse.

Since the legs are and this means that and

Also, since the hypotenuse is , this means that .

Start with the Pythagorean theorem.

Plug in , ,

Square to get .

Square to get .

Combine like terms.

Rearrange the equation.

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

Simplify the square root.

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Answer:

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

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