Question

Solve the triangle ABC, if the triangle exists. A=42.5° a=8.3 m b= 10.2 m Select the correct choice below and fill in the answer boxes within the choice. O O A. There are 2 possible solutions for the triangle. The measurements for the solution with the longer side c are as follows. mZB= mZC= The length of side c= (Round to the nearest (Round to the nearest (Round to the nearest tenth as tenth as needed.) tenth as needed.) needed.) The measurements for the solution with the shorter side care as follows. mZB mZC= The length of side c= ( Dund ta tha nnarnet (Dond to thn nnornet /Dound to thn nnarnet tonth ac Click to select and enter your answer(s). Previous

Answer 1

SOLA Critron A=42.5 8.3 m cb = 10.2 m use law af Sines to calculate the rest C Ы Sim B Sin A Sinc c 8.3 sin (42.5°) do. 2 Sin B sine 10.2 8.3 O, 6755go Sin B Sinc 8.3 10.2 s ) 0.675590 SinB SimB 10.2 * 0.67 5590 8.3 Sim B 6.89 2018 8.3 B Sin (0.830243) a В 11 56. 1237

Here ambiguity Ocen and B 180° - 56.1237 123.8763 Sin (56.1237) = sin (223.8763) So, ralue af Too possible solution is possible case ti 1 A = 42.5° B = 56.2237. 180° - (42-5+56-1237) – 81-3763 a = 8.3m cb = 10.2 m > Sinc 10.2 (from ) Sin B A Sin 182.3763) * 10.2 sim (56-1237) 0.988694 * 10.2 0-830242 12-1466 ) case 2: - A = 42.5, B = 123.8763 C 180"-(4-2-5+123-8763) 13.6237

a = 8.3m b= 10.2 m C Sinc * 10.2 Sin B Sint 13.6237) f 10.2 Sim | 123.8763) 0.235544 of 10.2 0.830242 2.8937 m

There are two possible solutions

Case 1:

$m \angle B=56.1\degree,m\angle C = 81.3 \degree,side \;c = 12.1m$

Case 2:

mZB = 123.8°, mZC= 13.6°, side c= 2.8m