### 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.

It is given that, Here we have to find the distance across the pond.

Answered: A surveyor uses the triangles shown in…

Math

Geometry

A surveyor uses the triangles shown in the diagram to measure the distance

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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Question

### 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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