To find the distance $A B$ across a river, a surveyor laid off a distance $B C=355 \mathrm{~m}$ on one side of the river. It is found that $\mathrm{B}=113^{\circ} 30^{\prime}$ and $\mathrm{C}=15^{\circ} 10^{\prime}$. Find $A B$. The distance $A B$ across the river is $\mathrm{m}$ (Simplify your answer. Do not round until the final answer. Then round to the nearest whole number as needed.)

Step 1 ：This problem is a trigonometry problem. We can use the Law of Sines to solve it. 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. In this case, we have a triangle ABC, where BC is known, and angles B and C are known. We want to find AB.

Step 2 ：We can set up the following equation using the Law of Sines: \(\frac{AB}{\sin(C)} = \frac{BC}{\sin(B)}\)

Step 3 ：We can solve this equation for AB. Given that B = 1.980948701013564, C = 0.26470826988580665, and BC = 355, we find that AB = 101.27781135452688

Step 4 ：Rounding to the nearest whole number, we find that the distance AB across the river is \(\boxed{101}\) meters.