Question 117736
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,-0.2,8),
locate(1,2,15)
)}}}

Since we can see that the triangle has legs of x and 8 with a hypotenuse of 15, 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+8^2=15^2}}}  Plug in a=x, b=8, and c=15. Now lets solve for x



{{{ x  ^ 2 + 6 4 = 2 2 5}}} Square each individual term




{{{ x  ^ 2 = 2 2 5 - 6 4}}} Subtract 64 from both sides



{{{ x  ^ 2 = 1 6 1}}} Combine like terms



{{{s q r t (  x  ^ 2 ) = s q r t ( 1 6 1 )}}} Take the square root of both sides



Which approximates to...

{{{x = 1 2 . 6 8 8 5 7 7 5 4 0 4 4 9 5}}}


So our answer is

{{{x = 1 2 . 6 8 8 5 7 7 5 4 0 4 4 9 5}}}



so the ladder can reach about 13 ft on the wall