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's how to solve the bearing problem: a) Find the bearing of Q from P Step 1: Identify the given bearing. The bearing of P from Q is 228^. Step 2: Calculate the back bearing. To find the bearing of Q from P, we use the rule for back bearings: if the bearing of A from B is , then the bearing of B from A is ± 180^. Since 228^ > 180^, we subtract 180^. Bearing of Q from P = 228^ - 180^ = 48^ The bearing of Q from P is 048^. b) Find the bearing of P from R Step 1: Determine the angle PQR. We are given that R is due south of Q. This means the line segment QR lies on the North-South line passing through Q. The bearing of P from Q is 228^. This angle is measured clockwise from the North line at Q to the line QP. The angle from the North line at Q to the South line at Q is 180^. Therefore, the angle between the South line (QR) and the line QP, which is PQR, is: PQR = 228^ - 180^ = 48^ Step 2: Determine the angle PRQ in triangle PQR. We know the sum of angles in a triangle is 180^. Given QPR = 72^. From Step 1, PQR = 48^. So, PRQ = 180^ - QPR - PQR PRQ = 180^ - 72^ - 48^ PRQ = 180^ - 120^ PRQ = 60^ Step 3: Determine the bearing of P from R. Since R is due south of Q, the line segment RQ points North from R. This means the North line at R is along RQ. The bearing of P from R is the angle measured clockwise from the North line at R (which is RQ) to the line segment RP. This angle is exactly PRQ. Therefore, the bearing of P from R is 60^. As a three-figure bearing, it is 060^. The bearing of P from R is 060^. That's 2 down. 3 left today — send the next one.