Question 280791
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,h),
locate(1,-0.2,5),
locate(1,2,15)
)}}}



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 {{{5}}} and {{{h}}} this means that {{{a=5}}} and {{{b=h}}}


   

Also, since the hypotenuse is {{{15}}}, this means that {{{c=15}}}.



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



{{{5^2+h^2=15^2}}} Plug in {{{a=5}}}, {{{b=h}}}, {{{c=15}}} 



{{{25+h^2=15^2}}} Square {{{5}}} to get {{{25}}}.



{{{25+h^2=225}}} Square {{{15}}} to get {{{225}}}.



{{{h^2=225-25}}} Subtract {{{25}}} from both sides.



{{{h^2=200}}} Combine like terms.



{{{h=sqrt(200)}}} Take the square root of both sides. Note: only the positive square root is considered (since a negative length doesn't make sense).



{{{h=10*sqrt(2)}}} <a href=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver>Simplify</a> the square root.



================================================================



Answer:



So the solution is {{{h=10*sqrt(2)}}} which approximates to {{{h=14.142}}} (using a calculator).



So the top of the ladder is approximately 14.142 ft above the floor.