Two poles of heights 6 m and 12 m stands on plane ground. If the distance between the feet of the poles be 8m, then find the distance between their tops.

Answer

To find the distance between the tops of two poles of heights 6 m and 12 m, standing 8 m apart, we can use the Pythagorean theorem. Here’s the step-by-step solution:

### Step 1: Identify the heights of the poles
Let the height of the first pole be \( h_1 = 6 \) m and the height of the second pole be \( h_2 = 12 \) m.

### Step 2: Calculate the vertical distance between the tops of the poles
The vertical distance between the tops of the two poles can be calculated as:
\[ \text{Vertical distance} = h_2 - h_1 = 12 \, \text{m} - 6 \, \text{m} = 6 \, \text{m} \]

### Step 3: Identify the horizontal distance between the poles
The horizontal distance between the feet of the poles is given as \( d = 8 \) m.

### Step 4: Apply the Pythagorean theorem
To find the distance between the tops of the poles, we can treat this as a right triangle where:
- One leg is the vertical distance (6 m),
- The other leg is the horizontal distance (8 m),
- The hypotenuse will be the distance between the tops of the poles.

Using the Pythagorean theorem:
\[ \text{Distance}^2 = \text{Vertical distance}^2 + \text{Horizontal distance}^2 \]
\[ \text{Distance}^2 = 6^2 + 8^2 \]
\[ \text{Distance}^2 = 36 + 64 \]
\[ \text{Distance}^2 = 100 \]

### Step 5: Calculate the distance
Taking the square root of both sides:
\[ \text{Distance} = \sqrt{100} = 10 \, \text{m} \]

### Final Answer
The distance between the tops of the two poles is \( 10 \, \text{m} \).

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