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.
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Here's how to calculate the bearings: First, let's determine the internal angles and bearings based on the given information. Given: F is due east of E. This means the line EF is horizontal. Angle GEF = 60^. Angle EFG = 40^. Step 1: Calculate the third angle in triangle EFG. The sum of angles in a triangle is 180^. EGF = 180^ - ( GEF + EFG) EGF = 180^ - (60^ + 40^) EGF = 180^ - 100^ EGF = 80^ Step 2: Determine the bearing of G from E. Draw a North line at E. Since F is due east of E, the line EF points East. The angle from North at E, clockwise to EF is 090^. From the diagram, G is below the line EF. Angle GEF is 60^. Therefore, the line EG is 60^ clockwise from the line EF. Bearing of G from E = (Bearing of F from E) + GEF Bearing (G from E) = 090^ + 60^ = 150^ Step 3: Determine the bearing of G from F. Draw a North line at F. Since E is due west of F, the line FE points West. The angle from North at F, clockwise to FE is 270^. From the diagram, G is below the line EF. Angle EFG is 40^. Therefore, the line FG is 40^ clockwise from the line FE. Bearing of G from F = (Bearing of E from F) + EFG Bearing (G from F) = 270^ + 40^ = 310^ a) Calculate the bearing of F from G. To find the bearing of F from G, we use the back bearing from G from F. If the bearing of A from B is : If < 180^, the bearing of B from A is + 180^. If > 180^, the bearing of B from A is - 180^. We have Bearing (G from F) = 310^. Since 310^ > 180^, the bearing of F from G is 310^ - 180^. Bearing (F from G) = 310^ - 180^ = 130^ This can also be found by drawing a North line at G and using parallel lines. The angle from North at F to FG is 310^. The angle from North at G to GF (alternate interior angle with the angle from the South line at F to FG) is 130^. b) Calculate the bearing of E from G. To find the bearing of E from G, we use the back bearing from G from E. We have Bearing (G from E) = 150^. Since 150^ < 180^, the bearing of E from G is 150^ + 180^. Bearing (E from G) = 150^ + 180^ = 330^ Final Answers: a) The bearing of F from G is 130^ b) The bearing of E from G is 330^ Send me the next one 📸