Use the figure to answer the questions below 0 6 in α (a) Express as a function of a. 0(a) = X in 19 in (b) If a = 64.65 °, determine 0. Round your answer to 2 decimal places. 0= (c) If a = 64.65 °, determine x. Round your answer to 2 decimal places. X=

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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### Use the figure to answer the questions below

The image depicts a right triangle with the following given dimensions and angles:
- The length of the side adjacent to angle \( \theta \) is 6 inches.
- The hypotenuse is 19 inches.
- Angle \( \alpha \) is adjacent to the side that is labeled \( x \), which is opposite to angle \( \theta \).

#### Tasks:

(a) **Express \( \theta \) as a function of \( \alpha \).**
- \(\theta(\alpha) = \underline{\hspace{3cm}}\)

(b) **If \( \alpha = 64.65^\circ \), determine \( \theta \). Round your answer to 2 decimal places.**
- \( \theta = \underline{\hspace{3cm}}^\circ\)

(c) **If \( \alpha = 64.65^\circ \), determine \( x \). Round your answer to 2 decimal places.**
- \( x = \underline{\hspace{3cm}} \) in

The diagram demonstrates fundamental trigonometric relationships to solve for angles and sides in a right triangle. Use trigonometric identities and functions to solve for the angle and the length of side \( x \) based on the given information.
Transcribed Image Text:### Use the figure to answer the questions below The image depicts a right triangle with the following given dimensions and angles: - The length of the side adjacent to angle \( \theta \) is 6 inches. - The hypotenuse is 19 inches. - Angle \( \alpha \) is adjacent to the side that is labeled \( x \), which is opposite to angle \( \theta \). #### Tasks: (a) **Express \( \theta \) as a function of \( \alpha \).** - \(\theta(\alpha) = \underline{\hspace{3cm}}\) (b) **If \( \alpha = 64.65^\circ \), determine \( \theta \). Round your answer to 2 decimal places.** - \( \theta = \underline{\hspace{3cm}}^\circ\) (c) **If \( \alpha = 64.65^\circ \), determine \( x \). Round your answer to 2 decimal places.** - \( x = \underline{\hspace{3cm}} \) in The diagram demonstrates fundamental trigonometric relationships to solve for angles and sides in a right triangle. Use trigonometric identities and functions to solve for the angle and the length of side \( x \) based on the given information.
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