This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the solutions to the questions: a) i) The distance and bearing of town D from school. Step 1: Establish a coordinate system with the school (S) at the origin (0, 0). • School (S): (0, 0) Step 2: Determine the coordinates of Town A. Town A is 160 km North of the school. • Town A: (0, 160) Step 3: Determine the coordinates of Town B. Town B is 100 km Westwards from Town A. • Town B: (0 - 100, 160) = (-100, 160) Step 4: Determine the coordinates of Town C. From Town B, the chairperson headed S75°W for 90 km. This means 75° West of South. The change in x-coordinate ( x) is negative (West), and the change in y-coordinate ( y) is negative (South). x = -90 (75^) y = -90 (75^) Using approximate values for (75^) ≈ 0.9659 and (75^) ≈ 0.2588: x = -90 × 0.9659 = -86.931 km y = -90 × 0