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B C 4 A Find cos(3) in the triangle. Choose 1 answer: 5 3.

B C 4 A Find cos(3) in the triangle. Choose 1 answer: 5 3.

Trigonometry (11th Edition)
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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### Problem Statement Given a right-angled triangle \(ABC\) with a right angle at \(C\), where: - \(AB = 5\) - \(AC = 4\) - \(BC = 3\) Find \(\cos(\beta)\) where \(\beta\) is the angle at vertex \(B\). ### Diagram Explanation The diagram shows a right-angled triangle \(ABC\): - The hypotenuse \(AB\) measures 5 units. - The side \(AC\) adjacent to angle \(\beta\) measures 4 units. - The side \(BC\) opposite angle \(\beta\) measures 3 units. ### Question Find \(\cos(\beta)\) in the triangle. Choose 1 answer: A. \(\dfrac{3}{4}\) B. \(\dfrac{4}{5}\) C. \(\dfrac{3}{5}\) D. \(\dfrac{4}{3}\) ### Solution For angle \(\beta\), use the cosine function defined as \(\cos(\beta) = \dfrac{\text{adjacent}}{\text{hypotenuse}}\). - Adjacent side to \(\beta\): \(AC = 4\) - Hypotenuse: \(AB = 5\) Thus, \(\cos(\beta) = \dfrac{4}{5}\). Therefore, the correct answer is: **B. \(\dfrac{4}{5}\)**
Transcribed Image Text:### Problem Statement Given a right-angled triangle \(ABC\) with a right angle at \(C\), where: - \(AB = 5\) - \(AC = 4\) - \(BC = 3\) Find \(\cos(\beta)\) where \(\beta\) is the angle at vertex \(B\). ### Diagram Explanation The diagram shows a right-angled triangle \(ABC\): - The hypotenuse \(AB\) measures 5 units. - The side \(AC\) adjacent to angle \(\beta\) measures 4 units. - The side \(BC\) opposite angle \(\beta\) measures 3 units. ### Question Find \(\cos(\beta)\) in the triangle. Choose 1 answer: A. \(\dfrac{3}{4}\) B. \(\dfrac{4}{5}\) C. \(\dfrac{3}{5}\) D. \(\dfrac{4}{3}\) ### Solution For angle \(\beta\), use the cosine function defined as \(\cos(\beta) = \dfrac{\text{adjacent}}{\text{hypotenuse}}\). - Adjacent side to \(\beta\): \(AC = 4\) - Hypotenuse: \(AB = 5\) Thus, \(\cos(\beta) = \dfrac{4}{5}\). Therefore, the correct answer is: **B. \(\dfrac{4}{5}\)**
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