7.2.59 Question Help Use the Law of Cosines to solve triangle ABC with B-148°, b

Question

7.2.59 Question Help Use the Law of Cosines to solve triangle ABC with B-148°, b= 10, and c=6. This is an ambiguous case of SSA. Use the Law of Cosines for side b. Substitute the values in the equation to obtain a quadratic equation in a. Find the roots of this equation and interpret the results. Again use the Law of Cosines to find A. Then find C-180°-A-B. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. (Round the final answer to the nearest tenth as needed. Round all intermediate values to the nearest tenth as needed.) O A. There is only one possible solution for the triangle. The measurements for the remaining angles A and C and side a are as follows. a- OB. There are 2 possible solutions for the triangle. The measurements for the solution with the longer side a are as follows. A1= The measurements for the solution with the shorter side a are as follows. C1= a1 = C2 a2 ° C. There are no possible solutions for this triangle

Explanation / Answer

there is only one solution

B = 148 , b = 10 , c = 6

applying law of sines

10 / sin 148 = 6 / sin C

C = 18.5 degrees

A = 180 - ( 18.5 + 148 )

A = 13.5 degrees

10 / sin 148 = a/ sin 13.5

a = 4.4

option A is correct

A = 13.5 , C = 18.5 , a = 4.4

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