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?

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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?

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Answer 1 · 2018-03-20T09:56:19

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

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

$h^{2} + {(3 ft)}^{2} = {(12 ft)}^{2}$ $h^2 + (3"ft")^2 = (12"ft")^2$

$h^{2} + 9 {ft}^{2} = 144 {ft}^{2}$ $h^2 + 9"ft"^2 = 144"ft"^2$

$h^{2} = 135 {ft}^{2}$ $h^2 = 135"ft"^2$

Take the square root to find the height:

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

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

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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

Explanation:

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