Question 316784
The ladder, the distance from the ladder base to the building, and the distance from the ground to the ladder on the building form a right triangle.
{{{drawing(300,300,-2,12,-2,12,line(0,0,0,10),locate(2.5,4.5,10),locate(1.9,-0.5,5),locate(-1.5,4,x),line(0,0.5,0.5,0.5),line(0.5,0.5,0.5,0),line(0,0,10,0),blue(line(4,0,0,8)))}}}
Use the Pythagorean theorem,
{{{x^2+5^2=10^2}}}
{{{x^2+25=100}}}
{{{x^2=75}}}
{{{x=sqrt(75)}}}
{{{highlight(x=5*sqrt(3))}}} or approximately,
{{{x=8.66}}} m