Establish a coordinate system.

To solve this problem, we will use trigonometry to determine the distances and bearings, which is the analytical equivalent of a precise scale drawing. Step 1: Establish a coordinate system. Let Abeokuta (Abc) be at the origin (0,0). We define North as the positive y-axis and East as the positive x-axis. Step 2: Determine the coordinates of Ikeja (IK). Ikeja is 60 km due South of Abeokuta. Therefore, the coordinates of Ikeja are (0, -60). Step 3: Calculate the displacement of Ibadan (Ib) from Ikeja. Ibadan is 110 km from Ikeja on a bearing of 036^. A bearing is measured clockwise from the North line. The eastward displacement (x-component) from Ikeja is given by 110 (36^). The northward displacement (y-component) from Ikeja is given by 110 (36^). Eastward displacement = 110 (36^) ≈ 110 × 0.5878 ≈ 64.658 km Northward displacement = 110 (36^) ≈ 110 × 0.8090 ≈ 88.990 km Step 4: Solve part b) - How far north and how far east Ibadan is from Ikeja. Based on the calculations in Step 3: • Ibadan is approximately 89.0 km North of Ikeja. • Ibadan is approximately 64.7 km East of Ikeja. Step 5: Determine the absolute coordinates of Ibadan (Ib) relative to Abeokuta. To find the coordinates of Ibadan relative to Abeokuta, we add the displacement from Ikeja to Ikeja's coordinates: x_Ibadan = x_Ikeja + Eastward displacement = 0 + 64.658 = 64.658 km y_Ibadan = y_Ikeja + Northward displacement = -60 + 88.990 = 28.990 km So, Ibadan's coordinates relative to Abeokuta are approximately (64.658, 28.990). Step 6: Solve part a) - The bearing and distance of Ibadan from Abeokuta. The distance of Ibadan from Abeokuta is the hypotenuse of the right-angled triangle formed by its coordinates: Distance = sqrt(x_Ibadan)^2 + y_Ibadan^2 Distance = sqrt((64.658)^2 + (28.990)^2) Distance