Solve the given problems. Sketch an appropriate figure,...

Solve the given problems. Sketch an appropriate figure, unless the figure is given.
In order to determine the length of a lake, a surveyor places poles in the ground at points $A, B,$ and $C$ and makes the measurements shown in Fig. 4.49. Determine the length of the lake, DE.

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Key Concepts

Proportional Reasoning

Proportional reasoning involves establishing and solving relationships between ratios. In the context of surveying, it is used to link measured distances and angles to unknown lengths, allowing for the computation of inaccessible distances by comparing proportional parts of similar figures.

Similar Triangles

Similar triangles are a key concept in many surveying problems, as triangles with identical corresponding angles have sides that are proportional. This proportionality enables the use of known lengths to determine unknown distances by setting up equivalent ratios between corresponding sides.

Indirect Measurement

Indirect measurement is a technique used to determine distances or lengths that are difficult or impossible to measure directly. By using measurements from accessible points and applying geometric or trigonometric principles, the desired unknown distance can be accurately computed.

Triangulation

Triangulation is a method commonly employed in surveying, where the measured angles from two or more known points are used to form triangles. With one or more side lengths known, the properties of these triangles allow for the calculation of unknown distances through the relationships between angles and sides.

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