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8 C 17 15 A Find sin(8) in the triangle.

8 C 17 15 A Find sin(8) in the triangle.

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
8th Edition
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Charles P. McKeague, Mark D. Turner
Chapter2: Right Triangle Trigonometry
Section: Chapter Questions
Problem 1RP: The origins of the sine function are found in the tables of chords for a circle constructed by the...
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Question
**Trigonometric Functions and Right Triangles** Below is an illustration of a right triangle labeled ABC, with angle β located at vertex B. - Length AB: 17 units - Length BC: 15 units - Length AC: 8 units The problem asks to determine the value of \( \sin(\beta) \) in the given triangle. ### Diagram Description The triangle ABC is a right triangle where: - \( \angle C \) is the right angle (90 degrees). - \( \angle \beta \) is located at vertex B. - Side opposite \( \angle \beta \) (side AC) is of length 8. - Side adjacent to \( \angle \beta \) (side BC) is of length 15. - Hypotenuse (side AB) is of length 17. ### Question and Choices: **Find** \( \sin(\beta) \) **in the triangle.** **Choose 1 answer:** (A) \( \frac{15}{8} \) (B) \( \frac{8}{17} \) (C) \( \frac{8}{15} \) (D) \( \frac{15}{17} \) ### Explanation: For a right triangle, the sine of an angle \( \beta \) is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. Thus, \[ \sin(\beta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{AC}{AB} = \frac{8}{17} \] The correct answer is: **(B) \( \frac{8}{17} \)**
Transcribed Image Text:**Trigonometric Functions and Right Triangles** Below is an illustration of a right triangle labeled ABC, with angle β located at vertex B. - Length AB: 17 units - Length BC: 15 units - Length AC: 8 units The problem asks to determine the value of \( \sin(\beta) \) in the given triangle. ### Diagram Description The triangle ABC is a right triangle where: - \( \angle C \) is the right angle (90 degrees). - \( \angle \beta \) is located at vertex B. - Side opposite \( \angle \beta \) (side AC) is of length 8. - Side adjacent to \( \angle \beta \) (side BC) is of length 15. - Hypotenuse (side AB) is of length 17. ### Question and Choices: **Find** \( \sin(\beta) \) **in the triangle.** **Choose 1 answer:** (A) \( \frac{15}{8} \) (B) \( \frac{8}{17} \) (C) \( \frac{8}{15} \) (D) \( \frac{15}{17} \) ### Explanation: For a right triangle, the sine of an angle \( \beta \) is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. Thus, \[ \sin(\beta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{AC}{AB} = \frac{8}{17} \] The correct answer is: **(B) \( \frac{8}{17} \)**
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