Step 1 :We are given that in triangle ABC, \(A=120.65^{\circ}\), \(C=33.28^{\circ}\), and \(c=100\).
Step 2 :We know that the sum of the angles in a triangle is 180 degrees. So we can calculate angle B by subtracting angles A and C from 180. This gives us \(B=180-120.65-33.28=26.07^{\circ}\).
Step 3 :We can use the law of sines to find the lengths of sides a and b. The law of sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.
Step 4 :We can set up the following equations to find a and b: \(a = \frac{c \cdot \sin(A)}{\sin(C)}\) and \(b = \frac{c \cdot \sin(B)}{\sin(C)}\).
Step 5 :Substituting the given values into these equations, we get \(a \approx 156.8\) and \(b \approx 80.1\).
Step 6 :\(\boxed{\text{Final Answer: The remaining sides of the triangle are } a \approx 156.8 \text{ and } b \approx 80.1}\)