Question

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?

Answer 1

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"`.