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
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
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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 (c) is equal to the sum of the squares of the other two sides (a and b). Here, the height the ladder reaches (12 feet) and the distance from the house to the base of the ladder (9 feet) are the two shorter sides.
We can set it up like this:
( a^2 + b^2 = c^2 )
Where:
– ( a = 12 ) feet (height)
– ( b = 9 ) feet (distance from the house)
– ( c ) is the length of the ladder we want to find.
Now we plug in the numbers:
( 12^2 + 9^2 = c^2 )
( 144 + 81 = c^2 )
( 225 = c^2 )
To find ( c ), we take the square root of 225:
( c = sqrt{225} = 15 ) feet.
So, the length of the ladder is 15 feet.
The correct answer is 15 ft! Keep practicing, and don’t hesitate to ask if you have more questions!