A15 foot ladder is leaning against a building .how high up on the building will the ladder reach when the bottom of the ladder is 6ft from the round your answer to the nearest tenth.[8.1]

The ladder is the hypotenuse of a right triangle.
one side=6ft
Height=.
EQUATION:
x^2+6^2=15^2
x^2=189
x=13.7 ft. (the ladder reaches 13.7 ft. up the wall)

This is just an application of Pythagoras' theorem. The ladder is the hypotenuse of a right triangle formed by the building. The Hypotenuse is 15 ft, and side a (the floor,) is 6 ft. PLugging this into the theorem, we get
15^2 = 6^2 + b^2
225 = 36 + b^2
189 = b^2
b is approximately 13.7478