A painter has a 24-foot ladder that he is using to paint a house. For safety reasons, the ladder must be placed at least 8 feet from the base of the side of the house. To the nearest tenth of a foot, how high can the ladder safely reach?

Pythagorean theorem

legnth of lader is hypotonuse (leaning against wall and wall is one leg and distance from wall to bottom of ladder is other leg)

so

a^2+b^2=c^2 where a and b are legs and c=hypotonuse

a=8

c=24

8^2+b^2=24^2

64+b^2=576

subtract 64

b^2=512

square root both sides

22.62

round to tenth

22.6

answer is 22.6 ft