录制这道题目的讲解视频---**Extraction Content:** **Question Stem:** 例1. 某景区有一人工湖，湖面有 A, B 两点，湖边架有直线型栈道 CD, 长为50m, 如图所示。现要测量 A, B 两点之间的距离，工作人员分别在 C, D 两点进行测量，在 C 点测得 ∠ACD = 45°, ∠BCD = 30°; 在 D 点测得 ∠ADB = 135°, ∠BDC = 120°。 (A, B, C, D 在同一平面内) 求 A, B 两点之间的距离; **Other Relevant Text:** * Location: Artificial lake in a scenic area. * Points on the lake: A, B. * Straight boardwalk: CD. * Length of boardwalk CD: 50m. * Measurement at point C: ∠ACD = 45°, ∠BCD = 30°. * Measurement at point D: ∠ADB = 135°, ∠BDC = 120°. * Condition: A, B, C, D are in the same plane. * Objective: Find the distance between points A and B. **Chart/Diagram Description:** * **Type:** Geometric figure, specifically a quadrilateral ACBD (or ADBC) with points A, B, C, D. It can also be seen as two triangles, △ACD and △BCD, sharing a common side CD. * **Main Elements:** * **Points:** Four distinct points labeled A, B, C, D. * **Lines/Segments:** Straight line segments connect: * A to C (AC) * A to D (AD) * B to C (BC) * B to D (BD) * C to D (CD) * **Relative Position:** Point D is located between points A and B in a visual sense, but within the quadrilateral ACBD. Points A and B appear on opposite sides of the line segment CD. Point C is at the bottom-left, D is central-top, A is top-left, B is top-right. The figure depicts a non-convex quadrilateral where the segment CD acts as a "base" for two triangles whose other vertices (A and B) are on opposite sides.