okay so this is a simple a^2 + b^2 = c^2 problem
we first draw a triangle with the "ladder" (long side) being 8' and the "slide" 10'
now we just have to find the distance between the two
so we have a^2 + 8^2 = 10^2
with me so far?
so now we simplify the equation we get a^2 + 64 = 100
now the next step is to isolate the a^2 so we get the 64 on to the other side
how do we get 64 on the other side?
yes!
how do we do that?
we subtract it, we have to do the opposite of the side
so in this case it is +64 so we do -64
if it was -64 we would do +64
got it?
okay so then we get
a^2 = 100-64
what is 100-64?
great!
so now we have
a^2 = 36
now we do the opposite of a number to the power
do you know what that is?
the opposite of a power is square root
so we have to find the square root of a^2
so then we would have
no, we would have
√a = √36
what is the square root of 36?
so what number times itself will get you 36?
so the answer is a = 6
and that is your answer
the horizontal distance is 6
I'm sorry