Determine the remaining sides and angles of the triangle $A B C$. \[ \mathrm{a}=200 \mathrm{~m}, \mathrm{~A}=33^{\circ} 54^{\prime}, \mathrm{C}=28^{\circ} 26^{\prime} \] What is the measure of angle B? \[ B= \] What is the length of side $b$ ? \[ \mathrm{b}= \] \[ \mathrm{m} \] (Do not round until the final answer. Then round to the nearest meter as needed.) What is the length of side $c$ ? \[ \mathrm{c}=\square \mathrm{m} \] (Do not round until the final answer. Then round to the nearest meter as needed.)

Step 1 ：We are given a triangle ABC with side a = 200m, angle A = 33 degrees 54 minutes, and angle C = 28 degrees 26 minutes. We are asked to find the measure of angle B, and the lengths of sides b and c.

Step 2 ：First, we can find angle B by subtracting the sum of angles A and C from 180 degrees, since the sum of angles in a triangle is 180 degrees.

Step 3 ：Next, we can use the law of sines to find the lengths of sides b and c. The law of sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is the same for all three sides of the triangle. Therefore, we can set up the following equations to find b and c: \(\frac{b}{\sin(B)} = \frac{a}{\sin(A)}\) and \(\frac{c}{\sin(C)} = \frac{a}{\sin(A)}\)

Step 4 ：We can solve these equations for b and c to find their lengths.

Step 5 ：Final Answer: The measure of angle B is \(\boxed{117.67}\) degrees. The length of side b is \(\boxed{318}\) meters. The length of side c is \(\boxed{171}\) meters.