Question 88645
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(-0.2,1.5,16),
locate(1,-0.2,x),
locate(1,2,25)
)}}}


Since we can see that the triangle has legs of 16 and x with a hypotenuse of 25, we can use Pythagoreans theorem to find the unknown side.



Pythagoreans theorem:


{{{a^2+b^2=c^2}}} where a and b are the legs of the triangle and c is the hypotenuse




{{{16^2+x^2=25^2}}}  Plug in a=16, b=x, and c=25. Now lets solve for x



{{{2 5 6 +  x  ^ 2 = 6 2 5}}} Square each individual term




{{{ x  ^ 2 = 6 2 5 - 2 5 6}}} Subtract 256 from both sides



{{{ x  ^ 2 = 3 6 9}}} Combine like terms



{{{s q r t (  x  ^ 2 ) = s q r t ( 3 6 9 )}}} Take the square root of both sides



{{{x=3*sqrt(41)}}} Simplify the square root



Which approximates to...

{{{x = 1 9 . 2 0 9 3 7 2 7 1 2 2 9 8 5}}}


So our answer is

{{{x = 1 9 . 2 0 9 3 7 2 7 1 2 2 9 8 5}}}



So the bottom of the ladder is about 19.21 feet from the building