Apainter has a 24ft ladder that he is using to paint a house. for safety reasons, the laddermust be placed at least 8 feet from the base of the side of the house. to the nearest tenthof a foot, how high can the ladder safely reach

If the 24 foot ladder is leaned on the house with the bottom 8 feet  from the base  the wall of the house, then it will form a right angled triangle.

The base of the triangle will be 8 feet while the 24 foot ladder forms the hypotenuse. We need to find out the height from the base of that wall to the point the ladder touches the wall.

Let the hypotenuse be C

Let the base be B

Let the height be A

We use this formula:   A squared + B squared = C squared

A sq + 8 sq = 24 sq

A sq + 64 = 576

A sq = 576 - 64

A sq = 512

A = Square root 512

A = 22.6

To the nearest 10th this will be 23

So the answer is 23 feet.