Campsites F and G are on opposite sides of a lake. A survey crew made the measurements shown on the diagram. What is the distance between the two campsites?

so this exact picture isn't the one on my test, but it would have to be greater than 38 because the line is longer. the question i got the measurement for the other side was 47. Hope this helps somebody :)

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akposevictor akposevictor · Answer 2 · 2021-11-05T15:56:33+01:00

Using the theorem of similar triangles, the distance between the two campsites is: 41.8 m.

Recall:

The ratio of the corresponding sides of two similar triangles are equal.

Thus, the diagram that shows the measurements made by the survey crew tells us that two similar triangles are formed.

Thus:

40.7/37 = 1.1

42.9/39 = 1.1

This shows the two sides are proportional. Since both triangles share a common angle, then the third side in each triangle will also be proportional to each other.

Therefore, if x represents the distance between the two campsites, we will have the following proportion:

[tex]\frac{x}{38} = 1.1[/tex]

Multiply both sides by 38

x = 41.8 m.

Therefore, using the theorem of similar triangles, the distance between the two campsites is: 41.8 m.

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