A ladder 10 m long reaches a window 8 m above the ground. Find the distance of the foot of the ladder from the base of the wall.

Answer

To solve the problem, we can use the Pythagorean theorem. The ladder, the wall, and the ground form a right triangle where:

- The length of the ladder is the hypotenuse (c).
- The height of the window is one leg of the triangle (a).
- The distance from the base of the wall to the foot of the ladder is the other leg of the triangle (b).

Given:
- Length of the ladder (c) = 10 m
- Height of the window (a) = 8 m

We need to find the distance (b) from the base of the wall to the foot of the ladder.

### Step 1: Apply the Pythagorean theorem
The Pythagorean theorem 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 lengths of the other two sides (a and b).

The formula is:
\[ c^2 = a^2 + b^2 \]

### Step 2: Substitute the known values
Substituting the known values into the equation:
\[ 10^2 = 8^2 + b^2 \]

### Step 3: Calculate the squares
Calculating the squares:
\[ 100 = 64 + b^2 \]

### Step 4: Rearrange the equation to solve for b²
Now, rearranging the equation to isolate \( b^2 \):
\[ b^2 = 100 - 64 \]

### Step 5: Simplify the right side
Calculating the right side:
\[ b^2 = 36 \]

### Step 6: Take the square root to find b
Taking the square root of both sides to find b:
\[ b = \sqrt{36} \]
\[ b = 6 \]

### Conclusion
The distance of the foot of the ladder from the base of the wall is **6 meters**.

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