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Find the distance between the driven and the sink, determine whether the work triangle shown is acute, right or obtuse and find the measure of the angle whose vertex is at the refrigerator (round your number to the nearest)

Find the distance between the driven and the sink, determine whether the work triangle shown is acute, right or obtuse and find the measure of the angle whose vertex is at the refrigerator (round your number to the nearest)

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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Find the distance between the driven and the sink, determine whether the work triangle shown is acute, right or obtuse and find the measure of the angle whose vertex is at the refrigerator (round your number to the nearest)
### Kitchen Triangular Layout Diagram This diagram depicts the layout of a kitchen, highlighting the placement of key appliances: the stove, refrigerator, and sink. The layout is organized in the form of a right triangle. #### Details of the Diagram: 1. **Appliances Placement:** - Stove: Located at the top right corner of the triangle. - Refrigerator: Positioned at the bottom left corner. - Sink: Placed at the bottom right corner. 2. **Dimensions:** - The distance between the stove and the refrigerator is labeled as 5 feet. - The distance between the stove and the sink is also 5 feet. - The distance between the refrigerator and the sink, forming the right angle and the base of the triangle, is labeled as 3 feet. The right angle is emphasized with a small square between the distance of the refrigerator and the sink, indicating a 90-degree angle. The diagram portrays the concept of the kitchen work triangle, which is a common kitchen design principle to reduce walking distance between these key appliances, thus improving efficiency.
Transcribed Image Text:### Kitchen Triangular Layout Diagram This diagram depicts the layout of a kitchen, highlighting the placement of key appliances: the stove, refrigerator, and sink. The layout is organized in the form of a right triangle. #### Details of the Diagram: 1. **Appliances Placement:** - Stove: Located at the top right corner of the triangle. - Refrigerator: Positioned at the bottom left corner. - Sink: Placed at the bottom right corner. 2. **Dimensions:** - The distance between the stove and the refrigerator is labeled as 5 feet. - The distance between the stove and the sink is also 5 feet. - The distance between the refrigerator and the sink, forming the right angle and the base of the triangle, is labeled as 3 feet. The right angle is emphasized with a small square between the distance of the refrigerator and the sink, indicating a 90-degree angle. The diagram portrays the concept of the kitchen work triangle, which is a common kitchen design principle to reduce walking distance between these key appliances, thus improving efficiency.
**Understanding Triangle Types Through Pythagorean Inequalities** Triangles can be categorized based on the relationship between the squares of their sides (denoted as \(a\), \(b\), and \(c\) with \(c\) being the longest side). This categorization uses the Pythagorean Theorem and its related inequalities. 1. **Obtuse Triangle** Inequality: \(a^2 + b^2 < c^2\) An **obtuse triangle** has one angle that measures more than 90 degrees. In such cases, the square of the longest side (\(c\)) is greater than the sum of the squares of the other two sides (\(a\) and \(b\)). Visual Representation: - Triangle with one angle greater than 90 degrees. 2. **Acute Triangle** Inequality: \(a^2 + b^2 > c^2\) An **acute triangle** has all angles less than 90 degrees. Here, the sum of the squares of the two shorter sides (\(a\) and \(b\)) is greater than the square of the longest side (\(c\)). Visual Representation: - Triangle with all angles less than 90 degrees. 3. **Right Triangle** Equality: \(a^2 + b^2 = c^2\) A **right triangle** has one angle exactly 90 degrees. It satisfies the Pythagorean Theorem where the sum of the squares of the two shorter sides equals the square of the longest side. Visual Representation: - Triangle with one 90-degree angle. These categorizations help in understanding fundamental properties and solving geometric problems involving triangles.
Transcribed Image Text:**Understanding Triangle Types Through Pythagorean Inequalities** Triangles can be categorized based on the relationship between the squares of their sides (denoted as \(a\), \(b\), and \(c\) with \(c\) being the longest side). This categorization uses the Pythagorean Theorem and its related inequalities. 1. **Obtuse Triangle** Inequality: \(a^2 + b^2 < c^2\) An **obtuse triangle** has one angle that measures more than 90 degrees. In such cases, the square of the longest side (\(c\)) is greater than the sum of the squares of the other two sides (\(a\) and \(b\)). Visual Representation: - Triangle with one angle greater than 90 degrees. 2. **Acute Triangle** Inequality: \(a^2 + b^2 > c^2\) An **acute triangle** has all angles less than 90 degrees. Here, the sum of the squares of the two shorter sides (\(a\) and \(b\)) is greater than the square of the longest side (\(c\)). Visual Representation: - Triangle with all angles less than 90 degrees. 3. **Right Triangle** Equality: \(a^2 + b^2 = c^2\) A **right triangle** has one angle exactly 90 degrees. It satisfies the Pythagorean Theorem where the sum of the squares of the two shorter sides equals the square of the longest side. Visual Representation: - Triangle with one 90-degree angle. These categorizations help in understanding fundamental properties and solving geometric problems involving triangles.
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