Explanation Given: The sides and the angle of the triangle are a = 5.240 , b = 4.446 and B = 48.13 ° . Formula used: If a, b and c are the lengths of the sides of the triangle and A, B and C are the three angles opposite to the sides of the triangle, then the law of sines is given by, a sin A = b sin B = c sin C . Procedure used: This is the case 2(Two sides and one angle) and so, the possibilities of the number of solutions are given by, No solution if b < a sin B . A right triangle solution if b = a sin B . Two solutions if a sin B < b < a . One solution if b > a . Calculation: The given values satisfy the condition (3). a sin B < b < a 5.240 sin 48.13 ° < 4.446 < 5.240 3.902 < 4.446 < 5.240 Thus, there would be two solutions. Use the law of sines to obtain the angle A . b sin B = a sin A 4.446 sin 48.13 ° = 5.240 sin A sin A = ( 5.240 ) ( sin 48.13 ° ) 4.446 sin A = ( 5.240 ) ( 0.744 ) 4.446 Solve ( 5.240 ) ( 0.744 ) 4.446 and take the sine inverse of it as follows. sin A = 3.898 4.446 A = sin − 1 ( 0.876 ) A = 61.36 ° The new angle A ′ in the second quadrant is given by, A ' = 180 ° − 61.36 ° A ' = 118.64 ° Find C and C ′ by use of the fact that sum of the interior angles of triangle is 180 ° . C = 180 ° − ( 61

11th Edition

ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Chapter 9.5, Problem 15E

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To solve: The triangle for the given values.

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