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Jse the Law of Sines to sol places. (If a triangle is not A = 56°, a = 10.4 %3D Case 1: (S C =

Jse the Law of Sines to sol places. (If a triangle is not A = 56°, a = 10.4 %3D Case 1: (S C =

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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## Law of Sines to Solve a Triangle ### Problem Statement Use the Law of Sines to solve the triangle. If two solutions exist, find both. Round your answers to two decimal places. (If a triangle is not possible, enter "IMPOSSIBLE" in each corresponding answer blank.) ### Given Data: - Angle \( A = 56^\circ \) - Side \( a = 10.4 \) - Side \( b = 12.2 \) ### Solution Format: #### Case 1: - \( B = \) ____° - \( C = \) ____° - \( c = \) ____ #### Case 2: - \( B = \) ____° - \( C = \) ____° - \( c = \) ____ (Note: Case 1 corresponds to the smaller B-value solution, and Case 2 corresponds to the larger B-value solution.) ### Explanation: If only one solution is possible, fill out Case 1 and mark Case 2 as "IMPOSSIBLE". If no solutions are possible, mark both cases as "IMPOSSIBLE". When solving, make sure to apply the Law of Sines appropriately: \[ \frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c} \] Use this ratio to determine the unknown angles and sides step-by-step. If you encounter any ambiguity (such as the SSA case), be sure to check whether a second triangle solution is valid.
Transcribed Image Text:## Law of Sines to Solve a Triangle ### Problem Statement Use the Law of Sines to solve the triangle. If two solutions exist, find both. Round your answers to two decimal places. (If a triangle is not possible, enter "IMPOSSIBLE" in each corresponding answer blank.) ### Given Data: - Angle \( A = 56^\circ \) - Side \( a = 10.4 \) - Side \( b = 12.2 \) ### Solution Format: #### Case 1: - \( B = \) ____° - \( C = \) ____° - \( c = \) ____ #### Case 2: - \( B = \) ____° - \( C = \) ____° - \( c = \) ____ (Note: Case 1 corresponds to the smaller B-value solution, and Case 2 corresponds to the larger B-value solution.) ### Explanation: If only one solution is possible, fill out Case 1 and mark Case 2 as "IMPOSSIBLE". If no solutions are possible, mark both cases as "IMPOSSIBLE". When solving, make sure to apply the Law of Sines appropriately: \[ \frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c} \] Use this ratio to determine the unknown angles and sides step-by-step. If you encounter any ambiguity (such as the SSA case), be sure to check whether a second triangle solution is valid.
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