Two pillars of heights 70 m and 20 m are standing 120 m apart . Find the distance between their tops .

Answer

To find the distance between the tops of the two pillars, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the heights of the pillars**:
- Let the height of the first pillar (A) be 70 m.
- Let the height of the second pillar (B) be 20 m.

2. **Determine the distance between the pillars**:
- The distance between the bases of the two pillars (AB) is given as 120 m.

3. **Calculate the vertical distance between the tops of the pillars**:
- The vertical distance (CD) between the tops of the two pillars can be calculated as:
\[ CD = \text{Height of pillar A} - \text{Height of pillar B} = 70 \, \text{m} - 20 \, \text{m} = 50 \, \text{m} \]

4. **Construct a right triangle**:
- We can visualize this scenario as a right triangle where:
- One leg (AE) is the horizontal distance between the two pillars, which is 120 m.
- The other leg (EC) is the vertical distance between the tops of the pillars, which we calculated as 50 m.

5. **Apply the Pythagorean theorem**:
- According to the Pythagorean theorem:
\[ AC^2 = AE^2 + EC^2 \]
- Substitute the known values:
\[ AC^2 = (120 \, \text{m})^2 + (50 \, \text{m})^2 \]
\[ AC^2 = 14400 \, \text{m}^2 + 2500 \, \text{m}^2 \]
\[ AC^2 = 16900 \, \text{m}^2 \]

6. **Calculate the distance AC**:
- Take the square root of both sides:
\[ AC = \sqrt{16900 \, \text{m}^2} = 130 \, \text{m} \]

### Final Answer:
The distance between the tops of the two pillars is **130 meters**.