The bottom of a ladder must be placed 3 feet from a wall. The ladder is 12 feet long. How far above the ground does the ladder touch the wall?

1 Answer
Mar 20, 2018

The height is approximately #11"ft" 7"in"#.

Explanation:

We generally (and should) use a ladder on level ground. So the ladder, wall and ground make a right triangle with the right angle between the wall and the ground.

Then the ladder is the hypoteneuse and has length #12 "ft"#. The section of ground between the ladder and the wall is one leg and has length #3"ft"#. Then the other leg, the height along the wall that the ladder reaches, is given by the Pythagorean Theorem:

#h^2 + (3"ft")^2 = (12"ft")^2#

#h^2 + 9"ft"^2 = 144"ft"^2#

#h^2 = 135"ft"^2#

Take the square root to find the height:

#h =\sqrt{135"ft"^2} = (3\sqrt{15})" ft" = 11.62"ft"# (to two decimal places).

The #0.62"ft"# multiplied by #12# inches per foot gives about #7# inches, thus the height is approximately #11"ft" 7"in"#.