Two triangles can be formed using the given measurements. Solve both triangles.
-$$\mathrm { A } = 58 ^ { \circ } , \mathrm { a } = 16 , \mathrm {~b} = 18$$
A) $\mathrm { B } = 72.6 ^ { \circ } , \mathrm { C } = 49.4 ^ { \circ } , \mathrm { c } = 14.3 ; \mathrm { B } = 107.4 ^ { \circ } , \mathrm { C } = 14.6 ^ { \circ } , \mathrm { c } = 4.8$
B) $\mathrm { B } = 17.4 ^ { \circ } , \mathrm { C } = 104.6 ^ { \circ } , \mathrm { C } = 18.3 ; \mathrm { B } = 162.6 ^ { \circ } , \mathrm { C } = 75.4 ^ { \circ } , \mathrm { c } = 18.3$
C) $\mathrm { B } = 17.4 ^ { \circ } , \mathrm { C } = 104.6 ^ { \circ } , \mathrm { C } = 14 ; \mathrm { B } = 162.6 ^ { \circ } , \mathrm { C } = 75.4 ^ { \circ } , \mathrm { C } = 14$
D) $\mathrm { B } = 72.6 ^ { \circ } , \mathrm { C } = 49.4 ^ { \circ } , \mathrm { c } = 17.9 ; \mathrm { B } = 107.4 ^ { \circ } , \mathrm { C } = 14.6 ^ { \circ } , \mathrm { c } = 17.9$

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Using the Law of Sines, we can find the possible values for angle B and subsequently angle C, since the sum of angles in a triangle is 180 degrees. The two solutions account for the ambiguous case in the Law of Sines, where two different triangles can be formed with the given information. The first set of angles and side lengths corresponds to the acute case, and the second set corresponds to the obtuse case.

Two Triangles Can Be Formed Using the Given Measurements A=58∘,a=16, b=18\mathrm { A } = 58 ^ { \circ } , \mathrm { a } = 16 , \mathrm {~b} = 18A=58∘,a=16, b=18

Two Triangles Can Be Formed Using the Given Measurements $\mathrm { A } = 58 ^ { \circ } , \mathrm { a } = 16 , \mathrm {~b} = 18$