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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**Task: Analyze the Right Triangle** **Objective:** Determine which statement or statements regarding the triangle are true. The right triangle satisfies the inequality: \(0 < a < b < c\). **Diagram:** - The right triangle has sides labeled \(a\), \(b\), and hypotenuse \(c\). - Angles are labeled \(\theta\) and \(\beta\), with \(\beta\) being the angle opposite side \(a\). **Statements to Evaluate:** - **A**: \(\sin(\theta) = \cos(\beta)\) - **B**: \(\tan(\theta) > \cos(\beta)\) - **C**: \(\tan(\theta) = \tan(\beta)\) - **D**: \(\sin(\beta) < \tan(\beta)\) - **E**: \(\sin(\beta) < \cos(\theta)\) **Choices:** - E - D - B - A - C Evaluate each trigonometric statement based on the properties of a right triangle.
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Transcribed Image Text:**Task: Analyze the Right Triangle** **Objective:** Determine which statement or statements regarding the triangle are true. The right triangle satisfies the inequality: \(0 < a < b < c\). **Diagram:** - The right triangle has sides labeled \(a\), \(b\), and hypotenuse \(c\). - Angles are labeled \(\theta\) and \(\beta\), with \(\beta\) being the angle opposite side \(a\). **Statements to Evaluate:** - **A**: \(\sin(\theta) = \cos(\beta)\) - **B**: \(\tan(\theta) > \cos(\beta)\) - **C**: \(\tan(\theta) = \tan(\beta)\) - **D**: \(\sin(\beta) < \tan(\beta)\) - **E**: \(\sin(\beta) < \cos(\theta)\) **Choices:** - E - D - B - A - C Evaluate each trigonometric statement based on the properties of a right triangle.
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