Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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### Measuring Distance Across a Pond Using Triangles **Scenario:** A surveyor uses the triangles shown in the diagram to measure the distance across a pond. **Details of the Method:** 1. The diagram consists of two overlapping triangles. 2. Each side length of the triangles is provided: - One triangle has side lengths of 29 feet, 41 feet, and another 29 feet. - The other triangle includes the side lengths of 41 feet, 52 feet, and one of the 29 feet sides overlaps with the first triangle’s 29 feet side. **Explanation of the Diagram:** - The two triangles are positioned such that they overlap, creating a larger composite shape. - The 41 feet side is shared between the two triangles in the diagram. - The overlapping triangles include points on the edges of a pond, allowing them to be used to calculate the distance across the pond without direct measurement across the water. **Question:** Using the given triangle dimensions in the diagram, what is the measured distance across the pond? **Options:** - 29 ft - 41 ft - 52 ft - cannot be determined **Understanding the Concept:** - To deduce the distance across the pond using the properties of similar triangles and the given measurements. **Answer:** (Please select the correct answer). This exercise demonstrates practical applications of geometry and triangle properties in real-world situations, like surveying land features.
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Transcribed Image Text:### Measuring Distance Across a Pond Using Triangles **Scenario:** A surveyor uses the triangles shown in the diagram to measure the distance across a pond. **Details of the Method:** 1. The diagram consists of two overlapping triangles. 2. Each side length of the triangles is provided: - One triangle has side lengths of 29 feet, 41 feet, and another 29 feet. - The other triangle includes the side lengths of 41 feet, 52 feet, and one of the 29 feet sides overlaps with the first triangle’s 29 feet side. **Explanation of the Diagram:** - The two triangles are positioned such that they overlap, creating a larger composite shape. - The 41 feet side is shared between the two triangles in the diagram. - The overlapping triangles include points on the edges of a pond, allowing them to be used to calculate the distance across the pond without direct measurement across the water. **Question:** Using the given triangle dimensions in the diagram, what is the measured distance across the pond? **Options:** - 29 ft - 41 ft - 52 ft - cannot be determined **Understanding the Concept:** - To deduce the distance across the pond using the properties of similar triangles and the given measurements. **Answer:** (Please select the correct answer). This exercise demonstrates practical applications of geometry and triangle properties in real-world situations, like surveying land features.
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