Solve the triangle ABC if the triangle exists Select the cor

Solve the triangle ABC, if the triangle exists. Select the correct choice below and fill in the answer boxes with in the choice. OA. There are 2 possible solutions for the triangle. The measurements for the solution with the longer side a are as follows. The measurements for the solution with the shorter side a are as follows.

Solution

HEre we first get the angle C, using sine formula, that is :

sin C/c = sin B/b

or sin C/7.302 = sin 155.2/14.069

or sin C/7.302 = 0.4195/14.069 = 0.0298

or sin C = 0.0298(7.302) =0.2177

or C= arcsin(0.2177) =12.57

or angle C = 12.57

and thus angle A + angle B+ angle C = 180 degree

or angle A + 155.2 + 12.57 =180

or angle A + 167.77 = 180

or angle A = 180 - 167.77 = 12.226           

Now on applying sine rule here we get

a/sin A = b/sin B

or a/sin 12.226 =14.069/sin 155.2 = 14.069/0.4195 = 33.5375

or a/0.2117 = 33.5375

or a = 33.537 x 0.2117 =   7.102

so correct answer is option B and all bolds are its answers.