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

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.2: Trigonometric Functions Of Angles
Problem 4E
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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