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A $12$ foot ladder leans against the side of a house, as shown in the figure above. The point of intersection between the ladder and the house is $9$ feet $6$ inches above the ground, and the base of the ladder is $2$ feet $6$ inches from the base of the house.

To the nearest inch, what length of the ladder, $x$, extends above the point where the ladder meets the house? (Calculator)

A

$1$ foot $11$ inches

B

$2$ feet $1$ inch

C

$2$ feet $2$ inches

D

$2$ feet $3$ inches

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