Anne and Bob are standing at the edge of a river. To use indirect measurement to determine how wide the river is, they choose a recognizable tree directly across from their position and designate it as T. Then, Bob and Anne move down the bank to point B and Anne continues down the river for the same distance to point C. Then she turns and walks perpendicular away from the river until she is can see both Bob and the tree. If Anne walked 25 feet, how wide is the river? What type of congruency rule did she and Bob use to determine the width?.
Anne and Bob are standing at the edge of a river. To use indirect measurement to determine how wide the river is, they choose a recognizable tree directly across from their position and designate it as T. Then, Bob and Anne move down the bank to point B and Anne continues down the river for the same distance to point C. Then she turns and walks perpendicular away from the river until she is can see both Bob and the tree. If Anne walked 25 feet, how wide is the river? What type of congruency rule did she and Bob use to determine the width?.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Anne and Bob are standing at the edge of a river. To use indirect measurement to determine how wide the river is, they choose a recognizable tree directly across from their position and designate it as T. Then, Bob and Anne move down the bank to point B and Anne continues down the river for the same distance to point C. Then she turns and walks perpendicular away from the river until she is can see both Bob and the tree. If Anne walked 25 feet, how wide is the river? What type of congruency rule did she and Bob use to determine the width?.
Transcribed Image Text:The image depicts a river scene with two people standing on the edge. The main elements in the image form a right triangle, used to demonstrate a geometrical concept:
1. **T**: The point at the top of a tree, across the river.
2. **A**: The point directly across from T on the near side of the river, where the observers are standing.
3. **B**: The point on the same side of the river as A, slightly to the right of it.
4. **C**: A point on the opposite side of the river from A and B, creating a right angle at point C.
5. **D**: Another point used to extend the line from C, passing through B.
- The line segments TA and AC are marked, highlighting the vertical and horizontal distances to establish the right angle at point C.
- The observers at point A are aligning their sight from points A and B towards the points T (top of the tree) and D, respectively.
- The problem or demonstration often involves using similar triangles or trigonometric ratios to find distances across the river, such as the width of the river or the height of the tree.
The diagram effectively illustrates the application of basic geometry concepts to solve practical problems, such as calculating distances or heights that are not directly measurable.
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