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
Step 1: Sketch the path and identify the points. Let point A be the origin. The man walks 5 km due north from A to an intermediate point, let's call it B. So, the coordinates of B relative to A are (0, 5). From B, he walks 4 km due west to point C. So, the coordinates of C relative to B are (-4, 0). Therefore, the coordinates of C relative to A are (-4, 5). This movement forms a right-angled triangle ABC, with the right angle at B. The length of side AB is 5 km (north). The length of side BC is 4 km (west). Step 2: Calculate the angle at A. We need to find the angle BAC, which is the angle between the North line (AB) and the line segment AC. In the right-angled triangle ABC: ( BAC) = opposite sideadjacent side = (BC)/(AB) ( BAC) = (4)/(5) Step 3: Calculate the value of the angle. BAC = ((4)/(5)) BAC ≈ 38.6598^ Step 4: Determine the bearing of C from A. Point C is located North-West of point A. The angle BAC is the angle measured from the North line (AB) towards the West. Bearings are measured clockwise from the North line (0^). For a point in the North-West quadrant, the bearing is 360^ minus the angle measured from the North line towards the West. Bearing of C from A = 360^ - BAC Bearing of C from A = 360^ - 38.6598^ Bearing of C from A = 321.3402^ Rounding to one decimal place, the bearing is 321.3^. The bearing of C from A is 321.3^. Send me the next one 📸