Question 110946
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,x),
locate(1,-0.2,5),
locate(1,2,13)
)}}}

Since we can see that the triangle has legs of x and 5 with a hypotenuse of 13, 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




{{{x^2+5^2=13^2}}}  Plug in a=x, b=5, and c=13. Now lets solve for x



{{{ x  ^ 2 + 2 5 = 1 6 9}}} Square each individual term




{{{ x  ^ 2 = 1 6 9 - 2 5}}} Subtract 25 from both sides



{{{ x  ^ 2 = 1 4 4}}} Combine like terms



{{{s q r t (  x  ^ 2 ) = s q r t ( 1 4 4 )}}} Take the square root of both sides




{{{x=12}}} Simplify the square root



So the ladder touches the 12 ft mark on the building