There is an obstacle in the form of a pond on the main chain...

There is an obstacle in the form of a pond on the main chain line AB . Two points C and D were taken on the opposite sides of the pond. On the left of CD, a line CE was laid out 65 m in length and a second line CF of 85 long was laid on the right of CD such that ECF are in a line. Determine the obstructed length $C D$. Given $E D=110 \mathrm{~m}$ and $\mathrm{DF}=120 \mathrm{~m}$.

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Key Concepts

Triangulation

Triangulation is a surveying method that uses the geometry of triangles to determine unknown distances. By measuring certain accessible distances and angles, surveyors can form triangles linking observable points to points that are difficult or impossible to measure directly, effectively bypassing obstructions.

Similar Triangles

Similar triangles are triangles that have the same shape but may differ in size, meaning their corresponding angles are equal and the sides are proportional. This geometric principle allows for the calculation of unknown lengths by setting up ratios between corresponding sides of triangles formed in the survey.

Proportional Reasoning

Proportional reasoning involves using ratios derived from similar geometric figures or parallel lines to compute unknown values. In surveying, this approach is critical for determining distances indirectly by relating measured segments to the segment of interest.

Obstruction Measurement Techniques

Obstruction measurement techniques encompass methods used to determine distances or dimensions that are hidden by obstacles. By taking measurements from strategically placed points around the obstacle and applying geometric principles such as triangulation and similar triangles, surveyors can accurately ascertain these hidden dimensions.

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