Question 117600
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(1,2,26)
)}}}

Since we can see that the triangle has legs of x and 8 with a hypotenuse of 26, 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=26^2}}}  Plug in a=x, b=8, and c=26. Now lets solve for x



{{{ x  ^ 2 + 6 4 = 6 7 6}}} Square each individual term




{{{ x  ^ 2 = 6 7 6 - 6 4}}} Subtract 64 from both sides



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



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




{{{x=6*sqrt(17)}}} Simplify the square root


Which approximates to...

{{{x = 2 4 . 7 3 8 6 3 3 7 5 3 7 0 6}}}


So our answer is

{{{x = 2 4 . 7 3 8 6 3 3 7 5 3 7 0 6}}}



So the ladder can reach about 24.74 feet