Determine the remaining sides and angles of the triangle $A B C$. \[ \mathrm{a}=100 \mathrm{~m}, \mathrm{~A}=39^{\circ} 54^{\prime}, \mathrm{C}=27^{\circ} 26^{\prime} \] What is the measure of angle $B$ ? \[ B=112^{\circ} 40^{\prime} \] What is the length of side $b$ ? \[ b=144 m \] (Do not round until the final answer. Then round to the nearest meter as needed) What is the length of side $c$ ? \[ c=\square m \] (Do not round until the final answer. Then round to the nearest meter as needed)

Step 1 ：We are given the lengths of sides a and b, and the measures of angles A, B, and C. We are asked to find the length of side c.

Step 2 ：We can use the Law of Sines to solve for side c. 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 3 ：So, we can set up the following equation using the Law of Sines: \(\frac{a}{\sin(A)} = \frac{c}{\sin(C)}\)

Step 4 ：We can rearrange this equation to solve for c: \(c = \frac{a \cdot \sin(C)}{\sin(A)}\)

Step 5 ：We can substitute the given values into this equation to find the length of side c.

Step 6 ：Given that a = 100, A = 0.6963863715457375, and C = 0.4788019914637778, we find that c = 72

Step 7 ：Final Answer: The length of side c is \(\boxed{72}\) meters.