If paula wants the tops of the latter to reach exactly 8 feet up the building, what is x, the distance between the building and the base of the latter in feet

6 ft

Step-by-step explanation:

Since the distance between the bottom of the ladder and the wall forms a right angle that is across from the ladder, you can use the Pythagorean Theorem to solve for the value of 'x':

a² + b² = c², where 'a' and 'b' are the legs of the triangle and 'c' is the diagonal or hypotenuse.  

Using 8 for 'a' and 10 for 'c':

8² + x² = 10²

64 + x² = 100

Subtract 64 from both sides:

64 - 64 + x² = 100 - 64 or x² = 36

Take the square root of both sides:

√x² = √36

x = 6 ft