Two poles of heights 6m and 11 m stand on plane ground. If the distance between their feet is 12 m, find the distance between their tops.

Answer

To solve the problem step by step, we will find the distance between the tops of the two poles.

### Step 1: Identify the heights of the poles and the distance between their feet.
- The height of the first pole (AB) = 11 m
- The height of the second pole (CD) = 6 m
- The distance between the feet of the poles (BD) = 12 m

### Step 2: Calculate the vertical distance between the tops of the poles.
- The vertical distance between the tops of the poles (AE) can be calculated as:
\[ AE = AB - CD = 11 \, \text{m} - 6 \, \text{m} = 5 \, \text{m} \]

### Step 3: Visualize the situation.
- We can visualize this as a right triangle where:
- One leg (AE) is the vertical distance between the tops of the poles (5 m).
- The other leg (BD) is the horizontal distance between the feet of the poles (12 m).

### Step 4: Apply the Pythagorean theorem to find the distance between the tops of the poles (AC).
- According to the Pythagorean theorem:
\[ AC^2 = AE^2 + BD^2 \]
Substituting the known values:
\[ AC^2 = 5^2 + 12^2 \]
\[ AC^2 = 25 + 144 \]
\[ AC^2 = 169 \]

### Step 5: Calculate AC.
- Taking the square root to find AC:
\[ AC = \sqrt{169} = 13 \, \text{m} \]

### Final Answer:
The distance between the tops of the two poles is **13 meters**.

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