The base of a 10​-foot ladder is 5 feet from a building. If the ladder reaches the flat​ roof, how tall is the​ building?

Answer 1

the 10 foot ladder is the hypotenuse of a right triangle with base = 5 feet

the triangle has sides in the ratio of 1-2-sqr3

or 5-10-5sqr3

5^2 + (5sqr3)^2 = 10^2

sum of the sides squared = square of the hypotenuse

the height of the building is 5sqr3 = about 5(1.732) = 8.66 feet tall