Question 175482

We basically have this triangle set up (note: you can rearrange the triangle):



{{{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(-0.2,1.5,18),
locate(1,-0.2,x),
locate(1,2,33)
)}}}



Since the legs are {{{18}}} and {{{x}}} this means that {{{a=18}}} and {{{b=x}}}


   

Also, since the hypotenuse is {{{33}}}, this means that {{{c=33}}}.



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



{{{18^2+x^2=33^2}}} Plug in {{{a=18}}}, {{{b=x}}}, {{{c=33}}} 



{{{324+x^2=33^2}}} Square {{{18}}} to get {{{324}}}.



{{{324+x^2=1089}}} Square {{{33}}} to get {{{1089}}}.



{{{x^2=1089-324}}} Subtract {{{324}}} from both sides.



{{{x^2=765}}} Combine like terms.



{{{x=sqrt(765)}}} Take the square root of both sides. Note: only the positive square root is considered (since a negative length doesn't make sense).



{{{x=3*sqrt(85)}}} Simplify the square root. (note: If you need help with simplifying square roots, check out this <a href=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)



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Answer:



So the solution is {{{x=3*sqrt(85)}}} which approximates to {{{x=27.659}}}.