The right triangle below satisfies 0< a cos(B) tan(0) = tan(B) sin(ß) < tan(ß) D sin(B) < cos(0) a O E O A O O

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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**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.
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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