If a ladder that is 10ft long is 6ft from the base of a wall How far up the wall does the ladder reach?

We have a right angled triangle. Apply Pythagoras.

l^(2) = b^(2) + h^(2)

h^(2) = l^(2) - b^(2)

Factor

h^(2) = (l - b)(l + b)

h^(2) = (10 - 6)(10 + 6)

h&(2) = 4(16)

h^(2) = 64

h = sqrt(64)

h = 8 ft.