A 45 foot ladder is used to clean the
gutters at your house. How far away from
the house should you put the ladder in
order for it to reach the 40 foot high
gutter? Round your answer to the nearest
tenth.
5 feet.

  20.6 feet

Step-by-step explanation:

The Pythagorean theorem can tell you the distance from the house the base of the ladder may be for it to reach 40 feet up. If that distance is represented by x, then it tells you ...

  45^2 = x^2 + 40^2

  x = √(2025 -1600) = √425

  x ≈ 20.6

The ladder will reach to 40 feet high when the base is 20.6 feet from the house.

Comment on ladder distance

The ladder safety association recommends an angle with the ground of about 75°. That corresponds to a distance from the house of about 10 feet. If the ladder is 20 feet away, it will barely reach the gutter, so placing it at that distance would probably not be safe.

An appropriate answer to this question is "10 feet", not based on math, but based on safety. At that distance the end of the ladder will extend about 3.7 feet beyond the gutter.