A ladder 8ft long leans against a wall. It rests on the ground 2 ft fromt he wall. How highon the wall does the ladder reach? and i am not taught the Pythagorean theorem.

Well here it is then:

c^2 = a^2 + b^2
where c is the side opposite the right angle.
In this case c is the length of the ladder, 8 ft.
so
a^2 + 2^2 = 64
a^2 = 60
a = sqrt 60 = sqrt (4*15)
= 2 sqrt 15
or approximately 7.75 ft