Question 135888
X^2+Y^2=20^2 OR X^2=20^2-Y^2 (X) BEING THE HEIGHT UP THE WALL & (Y) BEING THE DISTANCE OF THE BOTTOM OF THE LADDER FROM THE BUILDING.
X^2+(Y-7)^2=15^2 OR X^2=15^2-(Y-7)^2
SETTING THE X^2 EQUATIONS EQUAL AND SOLVE FOR Y:
20^2-Y^2=15^2-(Y-7)^2
400-Y^2=225-Y^2+14Y-49
400=225+14Y+49
14Y=400-225+49
14Y=224
Y=224/14
Y=16 FEET IS THE DISTANCE FROM THE WALL TO THE BOTTOM OF THE 20 FOOT LADDER.
X^2+16^2=20^2
X^2+256=400
X^2=400-256
X^2=144
X=SQRT144
X=12 FEET IS THE DISTANCE UP THE WALL.
PROOF
(16-7)^2+12^2=225
9^2+144=225 
81+144=225
225=225