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. Two poles of 8m and 14m stand upright on a plane ground. If the distance between two tops is 10m.
Find the distance between their feet.
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. Two poles of 8m and 14m stand upright on a plane ground. If the dist...
Understanding the Problem
To find the distance between the feet of two poles standing upright, we can visualize the situation as a right triangle. The heights of the poles and the distance between their tops form the sides of the triangle.
Given Information
- Height of the first pole (h1) = 8m
- Height of the second pole (h2) = 14m
- Distance between the tops of the poles = 10m
Calculating the Height Difference
- The height difference between the two poles is calculated as:
- Height difference (h) = h2 - h1 = 14m - 8m = 6m
Visualizing the Triangle
- We can now draw a right triangle where:
- The vertical side represents the height difference (6m).
- The horizontal side represents the distance between the feet of the poles (let's call it d).
- The hypotenuse represents the distance between the tops of the poles (10m).
Applying the Pythagorean Theorem
- According to the Pythagorean theorem:
- (hypotenuse)² = (height difference)² + (distance between feet)²
- Plugging in the values:
- 10² = 6² + d²
- 100 = 36 + d²
- d² = 100 - 36
- d² = 64
- d = √64
- d = 8m
Conclusion
The distance between the feet of the two poles is 8 meters. This geometric approach helps to visualize and solve the problem effectively.
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