The height at which the ladder touches the building is required.
The height of building where the ladder touches the building is 30.9 feet.
a = Required height
b = Distance between the bottom of the ladder and the base of the building = 8.5 feet
c = Length of ladder = 32 feet
From the Pythagoras theorem we have
[tex]a^2+b^2=c^2\\\Rightarrow a=\sqrt{c^2-b^2}\\\Rightarrow a=\sqrt{32^2-8.5^2}\\\Rightarrow a=30.9\ \text{feet}[/tex]
Learn more about Pythagoras theorem:
https://brainly.com/question/343682
