A ladder 10 feet long leans against a building the base of the ladder is 6 feet how high is the paint where the ladder touches the building

Use Pythagorean Theorem; a^2+b^2=c^2, where b^2 is the height you are looking for. so solve for b after plugging in a=6 and c=10.

SO;

(6)^2 + (b)^ = (10)^2
Then
36 + (b)^2 = 100
Next subtract 36 from both sides
(b)^2 = 64
Then take the Square root of both sides
b = SQRT(64)
b = 8ft high