Answer: 7.9 ft.
Step-by-step explanation:
Given : The length of ladder = 12 ft.
The distance of bottom of the ladder from the side of the house = 9^29 ft.
Since the side of the house must be standing vertical to the ground makinf right angle, then the triangle made by ladder must be a right angle with hypotenuse (Side opposite to right angle) = 12 ft.
Let x be the height of the top of the ladder from the ground.
Using the Pythagoras theorem of right triangles, we have
[tex]12^2=9^2+x^2\\\\\Rightarrow\ x^2=144-81\\\\\Rightarrow\ x^2=63\\\\\Rightarrow\ x=\sqrt{63}=7.9372539331\approx7.9[/tex]
Hence, the height of the top of the ladder from the ground = 7.9 ft.
