請教如何解這一題數學---**Textual Information:** **Question Stem:** 如下圖, A, B 兩點分別位於一河口的兩岸邊。某人在通往 A 點的筆直公路上, 距離 A 點 50 公尺的 C 點與距離 A 點 200 公尺的 D 點, 分別測得 ∠ACB=60°, ∠ADB=30°, 則 A 與 B 的距離為幾公尺? **(English Translation of Question Stem for clarity, not to be included in the output unless requested):** As shown in the figure below, points A and B are located on opposite banks of a river mouth. A person on a straight road leading to point A measures the angles ∠ACB = 60° and ∠ADB = 30° at point C, which is 50 meters from point A, and at point D, which is 200 meters from point A. What is the distance between A and B in meters? **Other Relevant Text:** - Distances from point A: - C is 50 meters from A. - D is 200 meters from A. - Measured angles: - ∠ACB = 60° - ∠ADB = 30° **Chart/Diagram Description:** * **Type:** Geometric diagram representing a surveying problem involving distances and angles. It shows a river and points on opposite banks and on a road. * **Main Elements:** * **Points:** Points labeled A, B, C, and D. A, C, and D are collinear on a horizontal line. B is located above the line containing A, C, and D. * **Lines:** * A thick solid line connects B to C and B to D, forming triangles ABC and ABD. * A dashed line connects B to A, appearing to be perpendicular to the line containing A, C, and D. This dashed line represents the distance AB. * A dashed line connects B to C. * A horizontal line segment is labeled with points A, C, and D in that order from left to right. * **Shapes:** Triangle ABC and Triangle ABD are formed. Triangle ABD appears to be a right-angled triangle at A based on the dashed line from B to A, although this is not explicitly stated as a right angle symbol. The dashed line BA suggests that AB is the perpendicular distance from B to the line AD. * **Coordinate Axes:** None present. * **Data Points/Series:** Not applicable. * **Angles:** * Angle ∠ACB is marked and labeled as 60°. It is located at point C in triangle ABC. * Angle ∠ADB is marked and labeled as 30°. It is located at point D in triangle ABD. * **Labels and Annotations:** Points A, B, C, D are labeled. Angle values 60° and 30° are labeled. * **Relative Position and Direction:** Points A, C, D are on a straight line. B is on the opposite side of the river from the line AD. The area above the line AD is shaded with wavy lines, representing the river. Points A, C, and D are on one bank (or a road leading to it), and B is on the opposite bank. Point C is between A and D on the line AD. * **Legend:** None present. * **River Representation:** The shaded area with wavy lines represents the river. Point B is on the river bank, and the line AD is on the other side, representing the road. **Other Diagrams:** There is another geometric figure to the right of the river diagram, which is a large equilateral triangle with smaller dashed equilateral triangles inside, resembling a fractal pattern (Sierpinski triangle). However, this figure is separate and not related to the question about the river and points A and B. Only the river diagram is relevant to the question asked.