The bottom of a ladder must be placed 5 ft. from a wall. The ladder is 12 feet long.
Based on the diagram, what is the distance in feet from the ground that the ladder reaches the wall? Round to the nearest tenth.
Using the Pythagorean theorem (a^2 + b^2 = c^2) where a = 5 ft., b = distance from the ground to where the ladder reaches the wall, and c = 12 ft. (the length of the ladder).
5^2 + b^2 = 12^2
25 + b^2 = 144
b^2 = 144 - 25
b^2 = 119
b = sqrt(119)
b ≈ 10.9 ft.
Therefore, the ladder reaches the wall at approximately 10.9 feet from the ground.