The top of a ladder rests at a height of 12 feet against the side of a house. If the base of the ladder is 9 feet from the house, what is the length of the ladder? Round to the nearest foot.
3 ft
11 ft
15 ft
21 ft
Calculating the Length of a Ladder Resting Against a House
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To find the length of the ladder, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the ladder, in this case) is equal to the sum of the squares of the other two sides (the height and the distance from the house).
Let ( a ) be the height (12 feet), ( b ) be the distance from the house (9 feet), and ( c ) be the length of the ladder.
According to the Pythagorean theorem:
[ c^2 = a^2 + b^2 ]
Substituting the values:
[ c^2 = 12^2 + 9^2 ]
[ c^2 = 144 + 81 ]
[ c^2 = 225 ]
Now take the square root of both sides to find ( c ):
[ c = sqrt{225} ]
[ c = 15 text{ feet} ]
So, the length of the ladder is 15 feet.