In Step 1, we calculate the distance AC, given that AC = 30m and (\tan 70^{\circ} = \frac{AC}{3}). Thus, AC = 3 * (\tan 70^{\circ}) = 3 * 2.75 = 8.25m. In Step 2, we find the distance BC, where (\tan 70^{\circ} = \frac{AC}{BC}), leading to BC = (\frac{AC}{\tan 70^{\circ}}) = (\frac{8.25}{2.75}) = 3m. In Step 3, we determine the width of the river, given by AB = BC + CM = 3m + 3m = 6m. Therefore, the width of the river is 6 meters.