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A 21-foot ladder is resting against a wall of a building in such a way that the top of the ladder is 11 feet above the ground. How far is the foot of the ladder from the base of the building?

The foot of the ladder is approximately $\square$ feet from the base of the building
(Round to the nearest foot as needed.)

Step 1 ：A 21-foot ladder is resting against a wall of a building in such a way that the top of the ladder is 11 feet above the ground. We are asked to find how far is the foot of the ladder from the base of the building.

Step 2 ：We can use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as: \(a^2 = b^2 + c^2\)

Step 3 ：In this case, the length of the ladder is the hypotenuse, the height from the ground to the top of the ladder is one side of the triangle, and the distance from the foot of the ladder to the base of the building is the other side of the triangle. We can plug these values into the Pythagorean theorem and solve for the unknown side.

Step 4 ：Let's denote the length of the ladder as \(a = 21\) feet, the height from the ground to the top of the ladder as \(b = 11\) feet, and the distance from the foot of the ladder to the base of the building as \(c\).

Step 5 ：Substituting these values into the Pythagorean theorem gives us: \(21^2 = 11^2 + c^2\).

Step 6 ：Solving this equation for \(c\) gives us: \(c = \sqrt{21^2 - 11^2}\).

Step 7 ：Calculating the square root gives us: \(c \approx 18\).

Step 8 ：So, the foot of the ladder is approximately 18 feet from the base of the building.

Step 9 ：Final Answer: The foot of the ladder is approximately \(\boxed{18}\) feet from the base of the building.