Measurement Session 5: Solutions

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A B C
Homework

Solutions for Session 5, Part A

See solutions for Problems: A1 | A2 | A3 | A4

Problem A1

Answers will vary. Here is one example:

The similarity ratio here is 5 m:1 cm. Here is the similar triangle:

The distance to the lighthouse (the length BC) is 53.5 m.

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Problem A2

The three measurements (angle, side, angle) determine a unique triangle; proving that two triangles are similar requires only two more measurements (the two angles in the second triangle). Also, as we've seen in Session 4, every polygon can be divided into triangles, which can be regarded as its basic building blocks. Therefore, triangles will work in every situation, which is why we use them instead of any other polygon.

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Problem A3

Using the same triangle, you could find the distance from your other sight point to the tree.

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Problem A4

Answers will vary, but here is one example: An indirect measurement can be taken when two figures are known to be similar and when a known measurement is taken from each figure. The ratio of this measurement establishes a scale factor for any other measurements that compare the two similar figures.

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Session 5 | Notes | Solutions | Video