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3 Using the figure below, find the measure of angle A. Round your answer to the nearest degree. Drawing is not to scale. 52 in A 65 in )+(x (E+Y A. 146° B. 124° 65° D. 56° 112 in

3 Using the figure below, find the measure of angle A. Round your answer to the nearest degree. Drawing is not to scale. 52 in A 65 in )+(x (E+Y A. 146° B. 124° 65° D. 56° 112 in

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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### Angle Calculation Problem **Problem Statement:** Using the figure below, find the measure of angle \( A \). Round your answer to the nearest degree. (Drawing is not to scale.) **Options:** - A. \( 146^\circ \) - B. \( 124^\circ \) - C. \( 65^\circ \) [Incorrect answer marked with a red 'X'] - D. \( 56^\circ \) **Figure Details:** The figure is a triangular shape with the following dimensions: - The side opposite angle \( A \) is labeled as 52 meters. - The side adjacent to angle \( A \) on the left is labeled as 65 meters. - The side adjacent to angle \( A \) on the right is labeled as 112 meters. To solve this problem, you may need to use trigonometric ratios or the law of cosines, considering the triangle's sides are given and an angle needs to be determined. **Explanation Involving Triangle:** 1. The triangle involves three sides with known lengths. 2. To find angle \( A \), one potential method is to use the Law of Cosines: \[ \cos(A) = \frac{b^2 + c^2 - a^2}{2bc} \] where \( a \), \( b \), and \( c \) are the sides of the triangle, with \( a \) being the side opposite the angle \( A \). The provided answer choices indicate the correct answer, excluding the marked incorrect option, should be found and cross-verified accordingly.
Transcribed Image Text:### Angle Calculation Problem **Problem Statement:** Using the figure below, find the measure of angle \( A \). Round your answer to the nearest degree. (Drawing is not to scale.) **Options:** - A. \( 146^\circ \) - B. \( 124^\circ \) - C. \( 65^\circ \) [Incorrect answer marked with a red 'X'] - D. \( 56^\circ \) **Figure Details:** The figure is a triangular shape with the following dimensions: - The side opposite angle \( A \) is labeled as 52 meters. - The side adjacent to angle \( A \) on the left is labeled as 65 meters. - The side adjacent to angle \( A \) on the right is labeled as 112 meters. To solve this problem, you may need to use trigonometric ratios or the law of cosines, considering the triangle's sides are given and an angle needs to be determined. **Explanation Involving Triangle:** 1. The triangle involves three sides with known lengths. 2. To find angle \( A \), one potential method is to use the Law of Cosines: \[ \cos(A) = \frac{b^2 + c^2 - a^2}{2bc} \] where \( a \), \( b \), and \( c \) are the sides of the triangle, with \( a \) being the side opposite the angle \( A \). The provided answer choices indicate the correct answer, excluding the marked incorrect option, should be found and cross-verified accordingly.
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