The ladder resting against the house forms a triangle similar to the one in the image below
To answer this question you must use Pythagorean theorem
[tex]a^{2} +b^{2}=c^{2}[/tex]
a and b are the legs (the sides that form a perpendicular/right angle)
c is the hypotenuse (the side opposite the right angle)
In this case...
a = x
b = 8
c = 34
^^^Plug these numbers into the theorem
[tex]x^{2} +8^{2} =34^{2}[/tex]
solve for x
[tex]x^{2}[/tex] + 64 = 1156
Subtract 64 to both sides
[tex]x^{2}[/tex] = 1092
Take the square root of both sides
x = √1092
This can be simplified to:
2√273
or
x ≈ 33.045...
The ladder reached roughly 33.05 ft up the wall of the building
Hope this helped!
~Just a girl in love with Shawn Mendes
