Answer:
6.7 feet
Explanation:
You want to know the height of a 9 ft ladder above the ground where it leans against a house, and its base is 6 ft from the house.
Pythagorean theorem
The Pythagorean theorem relates the side length of a right triangle. The geometry of this problem can be modeled by a right triangle with hypotenuse 9 ft and one leg 6 ft.
a² +b² = c² . . . . sum of the squares of the legs is the square of the hypotenuse
6² +b² = 9²
b² = 81 -36 = 45
b = √45 ≈ 6.708
The top of the ladder is about 6.7 feet above the ground.