Question 251544
After drawing the picture, we basically have this triangle set up:



{{{drawing(500,500,-0.5,2,-0.5,3.2,
line(0,0,0,3),
line(0,3,2,0),
line(2,0,0,0),
locate(-0.2,1.5,7),
locate(1,-0.2,24),
locate(1,2,x)
)}}}



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



Remember, the Pythagorean Theorem is {{{a^2+b^2=c^2}}} 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^2+b^2=c^2}}} Start with the Pythagorean theorem.



{{{7^2+24^2=x^2}}} Plug in {{{a=7}}}, {{{b=24}}}, {{{c=x}}} 



{{{49+24^2=x^2}}} Square {{{7}}} to get {{{49}}}.



{{{49+576=x^2}}} Square {{{24}}} to get {{{576}}}.



{{{625=x^2}}} Combine like terms.



{{{x^2=625}}} Rearrange the equation.



{{{x=sqrt(625)}}} 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.