Question 128908
Pythagoras says {{{c^2=a^2+b^2}}}.  The ladder itself is c, and the distance from the foot of the ladder to the base of the vertical wall is either a or b, as you please, so:


{{{13^2=3^2+b^2}}}


{{{b^2 = 169 - 9}}}


{{{b^2= 160}}}


{{{b= sqrt(160)}}}


{{{b=sqrt(16*10)}}}


{{{b=4*sqrt(10)}}}


So the ladder reaches {{{4*sqrt(10)}}} meters up the wall.  Roughly 12.6 meters.


By the way, that is a HUGE ladder, over 42 and a half feet long. It would reach to the 4th floor of most multi-story buildings.