Solve the triangle ABC, if the triangle exists A:43.5° a-8.4 m b:10.7 m Select t

Question

Solve the triangle ABC, if the triangle exists A:43.5° a-8.4 m b:10.7 m Select the correct choice below and fill in the answer boxes within the choice O A. There is only 1 possible solution for the triangle The measurements for the remaining angles B and C and side c are as follows (Round to the nearest tenth as needed.) (Round to the nearest tenth as needed.) The length of side c (Round to the nearest tenth as needed O B. There are 2 possible solutions for the triangle The measurements for the solution with the longer side c are as follows The length of side c (Round to the nearest (Round to the nearest (Round to the nearest tenth as tenth as needed The measurements for the solution with the shorter side c are as follows tenth as needed needed (Round to the nearest tenth as needed.) (Round to the nearest tenth as needed.) The length of side c (Round to the nearest tenth as needed.) O C. There are no possible solutions for this triangle

Explanation / Answer

A = 43.5 , a = 8.4 , b = 10.7

there are two solutions

applying law of sines

8.4 / sin 43.5 = 10.7 / sin B

B = 61.3 degrees

C = 180 - ( 61.3 + 43.5) = 75.2 degrees

8.4 / sin 43.5 = c / sin 75.2

c = 11.8 m

measurements of shorter c side

B = 118.7 degrees

C = 180 - ( 118.7 + 43.5 )

C = 17.8 degrees

8.4 / sin 43.5 = c / sin 17.8

c = 3.7 m

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