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Shore Riv xft 50 ft SA 30 ft 80 ft

Shore Riv xft 50 ft SA 30 ft 80 ft

Elementary Geometry For College Students, 7e
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

Find the distance represented by x

### River Crossing Problem In this diagram, we analyze a typical river crossing scenario where the objective is to calculate certain dimensions involved. #### Description of Diagram - **Shore**: There are two shorelines on either side of the river. - **River**: This is the body of water flowing between the two shores. - **x ft**: This is the distance along the shore on the right-hand side of the river, which needs to be determined. - **80 ft**: This is the horizontal span across the river and part of the adjacent shorelines. - **50 ft**: This distance is from a point on the shore to another point on the river. - **30 ft**: This is the vertical distance from one shore down to a point that intersects the river. #### Triangle Relationships The central focus is on the right-angled triangles formed by intersecting lines along the river shores: - A right triangle is formed by the vertical distance of 30 ft, the horizontal span of 80 ft, and a hypotenuse which constitutes the river crossing solution. To solve for the unknown \(x\), you can use the Pythagorean theorem, or trigonometric principles depending on the exact problem constraints provided. ### Educational Objectives - Understanding real-world applications of the Pythagorean theorem. - Solving for unknown distances in geometric shapes. - Applying theorems and formulas to practical scenarios. This type of problem helps reinforce fundamental concepts in geometry and trigonometry through practical application.
Transcribed Image Text:### River Crossing Problem In this diagram, we analyze a typical river crossing scenario where the objective is to calculate certain dimensions involved. #### Description of Diagram - **Shore**: There are two shorelines on either side of the river. - **River**: This is the body of water flowing between the two shores. - **x ft**: This is the distance along the shore on the right-hand side of the river, which needs to be determined. - **80 ft**: This is the horizontal span across the river and part of the adjacent shorelines. - **50 ft**: This distance is from a point on the shore to another point on the river. - **30 ft**: This is the vertical distance from one shore down to a point that intersects the river. #### Triangle Relationships The central focus is on the right-angled triangles formed by intersecting lines along the river shores: - A right triangle is formed by the vertical distance of 30 ft, the horizontal span of 80 ft, and a hypotenuse which constitutes the river crossing solution. To solve for the unknown \(x\), you can use the Pythagorean theorem, or trigonometric principles depending on the exact problem constraints provided. ### Educational Objectives - Understanding real-world applications of the Pythagorean theorem. - Solving for unknown distances in geometric shapes. - Applying theorems and formulas to practical scenarios. This type of problem helps reinforce fundamental concepts in geometry and trigonometry through practical application.
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