Find the Missing Parts of the Triangle $$\begin{array} { l } \mathrm { C } = 35 ^ { \circ } 30 ^ { \prime } \\\mathrm { a } = 18.76 \\\mathrm { c } = 16.15\end{array}$$

Find the missing parts of the triangle.
- $$\begin{array} { l } \mathrm { C } = 35 ^ { \circ } 30 ^ { \prime } \\\mathrm { a } = 18.76 \\\mathrm { c } = 16.15\end{array}$$
If necessary, round side lengths to the nearest hundredth.

A) $\mathrm { A } = 42 ^ { \circ } 25 ^ { \prime } , \mathrm { B } = 102 ^ { \circ } 05 ^ { \prime } , \mathrm { b } = 25.19$
B) $\mathrm { A } _ { 1 } = 42 ^ { \circ } 25 ^ { \prime } , \mathrm { B } _ { 1 } = 102 ^ { \circ } 05 ^ { \prime } , \mathrm { b } _ { 1 } = 27.2$ ;
$$\mathrm { A } _ { 2 } = 137 ^ { \circ } 35 ^ { \prime } , \mathrm { B } _ { 2 } = 6 ^ { \circ } 55 ^ { \prime } , \mathrm { b } _ { 2 } = 3.35$$
C) no such triangle
D) $\mathrm { A } _ { 1 } = 102 ^ { \circ } 05 ^ { \prime } , \mathrm { B } _ { 1 } = 42 ^ { \circ } 25 ^ { \prime } , \mathrm { b } _ { 1 } = 17.52$ ;
$\mathrm { A } _ { 2 } = 6 ^ { \circ } 55 ^ { \prime } , \mathrm { B } _ { 2 } = 137 ^ { \circ } 35 ^ { \prime } , \mathrm { b } _ { 2 } = 26.19$