Find the Missing Parts of the Triangle $\mathrm { A } = 75 ^ { \circ } , \mathrm { C } = 45 ^ { \circ } , \mathrm { c } = 5 \sqrt { 3 } + 5$

Multiple Choice

Find the missing parts of the triangle.
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If necessary, round angles to the nearest degree and give exact values of side lengths.

A) $\mathrm { A } = 75 ^ { \circ } , \mathrm { C } = 45 ^ { \circ } , \mathrm { c } = 5 \sqrt { 3 } + 5$
B) no such triangle
C) $\mathrm { A } = 45 ^ { \circ } , \mathrm { C } = 75 ^ { \circ } , \mathrm { c } = 5 \sqrt { 3 }$
D) $\mathrm { A } = 45 ^ { \circ } , \mathrm { C } = 75 ^ { \circ } , \mathrm { c } = 5 \sqrt { 3 } + 5$