Question 316999
We basically have this triangle set up:



{{{drawing(500,500,-0.5,2,-0.5,1.2,
line(0,0,0,0.5),
line(0,0.5,2,0),
line(2,0,0,0),
locate(-0.1,0.3,4),
locate(1,-0.1,43),
locate(1,0.4,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 {{{4}}} and {{{43}}} this means that {{{a=4}}} and {{{b=43}}}


   

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



{{{a^2+b^2=c^2}}} Start with the Pythagorean theorem.



{{{4^2+43^2=x^2}}} Plug in {{{a=4}}}, {{{b=43}}}, {{{c=x}}} 



{{{16+43^2=x^2}}} Square {{{4}}} to get {{{16}}}.



{{{16+1849=x^2}}} Square {{{43}}} to get {{{1849}}}.



{{{1865=x^2}}} Combine like terms.



{{{x^2=1865}}} Rearrange the equation.



{{{x=sqrt(1865)}}} Take the square root of both sides. Note: only the positive square root is considered (since a negative length doesn't make sense).



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Answer:



So the solution is {{{x=sqrt(1865)}}} which approximates to {{{x=43.186}}}.


So the ramp is about 43.186 ft long.