What is the measure of Angle B? **Title: Calculating Angles Using the Law of Sines****Introduction to the Problem:**Chau and Donna are standing on a riverbank, 180 meters apart, at points \(A\) and \(B\) respectively. Donna is 230 meters from a house located across the river at point \(C\). Suppose that angle \(A\) (angle \(BAC\)) is \(49^\circ\). What is the measure of angle \(B\) (angle \(ABC\))? Round your answer to the nearest tenth of a degree.**Diagram Explanation:**In the provided diagram:- Points \(A\) and \(B\) are on the riverbank, separated by a distance of 180 meters.- Point \(C\) represents the location of a house across the river.- The line segment \(AC\) forms an angle of \(49^\circ\) with line segment \(AB\).- The distance from point \(B\) to point \(C\) is marked as 230 meters.- The diagram visually represents the problem with horizontal and vertical lines showing their respective measurements.**Using the Law of Sines:**To find the measure of angle \(B\), we can apply the Law of Sines, which states:\[\frac{\sin(A)}{a} = \frac{\sin(B)}{b} = \frac{\sin(C)}{c}\]Where:- \(A = 49^\circ\)- \(a = BC = 230 \text{ meters}\)- \(b = AC\)Given that \(AB = 180\) meters, \(A = 49^\circ\), and \(BC = 230\) meters, we can set up the equation as follows to solve for angle \(B\):\[\frac{\sin(49^\circ)}{230} = \frac{\sin(B)}{180}\]Solving for \(\sin(B)\):\[\sin(B) = \frac{180 \times \sin(49^\circ)}{230}\]After calculating the right-hand side:\[\sin(B) \approx \frac{180 \times 0.7547}{230}\]\[\sin(B) \approx 0.5904\]Taking the inverse sine:\[B \approx \sin^{-1}(0.590

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Chau and Donna are standing on a riverbank, 180 meters apart, at points A and B respectively. (See the figure below.) Donna is 230 meters from a house located across the river at point C. Suppose that angle A (angle BAC) is 49°. What is the measure of angle B (angle AB C)? Round your answer to the nearest tenth of a degree. 180 m 49° 230 m 44 4

Chau and Donna are standing on a riverbank, 180 meters apart, at points A and B respectively. (See the figure below.) Donna is 230 meters from a house located across the river at point C. Suppose that angle A (angle BAC) is 49°. What is the measure of angle B (angle AB C)? Round your answer to the nearest tenth of a degree. 180 m 49° 230 m 44 4

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section: Chapter Questions

Problem 2T

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