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
You're on a roll — Step 1: Sketch the path and identify the points. Let point A be the starting point. The man walks 5 km due north from A to an intermediate point, let's call it B. From B, he walks 4 km due west to point C. This movement forms a right-angled triangle ABC, with the right angle at B. The side AB represents the Northward movement (5 km). The side BC represents the Westward movement (4 km). Step 2: Calculate the angle at A. We need to find the angle BAC, which is the angle measured from the North line (AB) towards the West. 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. Bearings are measured clockwise from the North line (0^). The angle BAC is the angle measured from the North line towards the West. To find the bearing, we subtract this angle from 360^ (since it's in the North-West quadrant). 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^. What's next?