Short Answer 
Triangulation is a geometric method for measuring unknown distances or heights by forming triangles with known points. In the flagpole problem, you create a right-angled triangle, DAB, using trigonometric ratios to relate known angles to the sides, but additional information like side lengths or the flagpole height is necessary to find the unknown distance AB.
Step 1: Understand the Concept of Triangulation
Triangulation is a method used in measurement and surveying to determine unknown distances or heights using geometry and trigonometry. In a typical triangulation problem, you form a triangle with known points and use angles and the lengths of sides to solve for unknown variables. In the context of the flagpole problem, you will create a triangle using points A, B, and D.
Step 2: Analyze the Triangle DAB
The triangle DAB is a right-angled triangle where certain angles are given: angle BDC is 30° and angle ADC is 45°. To calculate unknown lengths, you will rely on trigonometric ratios, especially the tangent, which relates an angle to the opposite and adjacent sides. This means you can use these angles to establish relationships between the sides AD and BD, which are crucial for determining the distance AB.
Step 3: Recognize Limitations
Despite the use of trigonometry, the problem cannot be solved without knowing additional details such as the lengths of sides AD or BD or the height of the flagpole. The lack of this information makes it impossible to accurately calculate the distance AB. Therefore, remember that having enough data is essential for utilizing triangulation effectively in problems like this one.