Two sides and an angle (SSA) of a triangle are given. Determine whether the give

Question

Two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements produce one triangle, two triangles, or no triangle at all. Solve each triangle that results a = 50.3, c = 38, A = 120 degree Selected the correct choice below and, if necessary, fill in the answer boxes to complete your choice. (Round side lengths to the nearest tenth and angle measurements to the nearest degree as needed.) A. There is only one possible solution for the triangle. The measurements for the remaining side b and angles C and B are as follows. C degree B degree b B. There are two possible solutions for the triangle. The measurements for the solution with the the smaller angle C are as follows. C_1 degree B_1 degree b_1 The measurements for the solution with the the larger angle C are as follows. C_2 degree B_2 degree b_2 C. There are no possible solutions for this triangle.

Explanation / Answer

a= 50 , c= 38, A = 120 degree

from law of sine:

sin A / a = sin B / b = sin C / c

from sin A / a = sin C / c

sin 120 / 50 = sin C / 38

C = 31.30 degree

or C' = 180 - 31. 30 = 148.690

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since A+B+C = 180

120 + B+31.30 = 180

B = 28.7 degree

when C' = 148.69

then 120 + B'+ 148.69 = 180

B' = -88.69 which is not possible.so there will be only one solution.

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from sin A / a = sin B / b

sin 120 / 50 = sin 28.7 / b

b = 27.72

so B = 28.7degree , b= 27.72 , C = 31.30degree

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