Answer:
28.4 units
Step-by-step explanation:
If we call the given angles C and A, then the given side is c, and the other two sides can be found from the Law of Sines.
Angle B is the remaining angle of the triangle:
180° -C -A = 180° -30° -45° = 105°
The remaining sides are ...
b = sin(B)/sin(C)·c = sin(105°)/sin(30°)·6√2 ≈ 16.4
a = sin(A)/sin(C)·c = sin(45°)/sin(30°)·6√2 = 12
Then the sum of the lengths of the remaining sides is ...
a + b = 12 + 16.4 = 28.4 . . . units
