A 13-m long ladder reaches a window of building 12 m above the ground. Determine the distance of the foot the ladder from the building.

Answer

To solve the problem, we can use the Pythagorean theorem, which relates the lengths of the sides of a right triangle. Here’s the step-by-step solution:

### Step 1: Identify the triangle
We have a right triangle formed by the ladder, the wall of the building, and the ground. The ladder acts as the hypotenuse, the height of the window is one leg, and the distance from the foot of the ladder to the building is the other leg.

### Step 2: Assign the lengths
- Length of the ladder (hypotenuse, AC) = 13 m
- Height of the window (one leg, BC) = 12 m
- Distance from the foot of the ladder to the building (the other leg, AB) = ?

### Step 3: Apply the Pythagorean theorem
According to the Pythagorean theorem:
\[ AC^2 = AB^2 + BC^2 \]

Substituting the known values:
\[ 13^2 = AB^2 + 12^2 \]

### Step 4: Calculate the squares
Calculating the squares:
- \( 13^2 = 169 \)
- \( 12^2 = 144 \)

Now substitute these values into the equation:
\[ 169 = AB^2 + 144 \]

### Step 5: Solve for AB^2
Rearranging the equation to solve for \( AB^2 \):
\[ AB^2 = 169 - 144 \]
\[ AB^2 = 25 \]

### Step 6: Find AB
Taking the square root of both sides to find AB:
\[ AB = \sqrt{25} \]
\[ AB = 5 \]

### Conclusion
The distance of the foot of the ladder from the building is **5 meters**.

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