1. **Problem statement:** We have triangle BFG with sides BF = 36 km, FG = 55 km, and angles at F and B given. We need to find: i) Bearing of B from F ii) Distance BG iii) Bearing of G from B 2. **Understanding bearings and angles:** - Bearing is measured clockwise from the north direction. - Angle at F is 103° between BF and FG. - Angle at B is 4° between vertical north and BG. 3. **Step i) Bearing of B from F:** - Given angle at F is 103°, which is the angle between north line at F and line BF. - Bearing of B from F = 103° (already given). 4. **Step ii) Calculate distance BG:** - Use Law of Cosines in triangle BFG: $$BG^2 = BF^2 + FG^2 - 2 \times BF \times FG \times \cos(\angle F)$$ - Substitute values: $$BG^2 = 36^2 + 55^2 - 2 \times 36 \times 55 \times \cos(103^\circ)$$ - Calculate: $$36^2 = 1296$$ $$55^2 = 3025$$ $$\cos(103^\circ) \approx -0.224951$$ - So: $$BG^2 = 1296 + 3025 - 2 \times 36 \times 55 \times (-0.224951)$$ $$BG^2 = 4321 + 2 \times 36 \times 55 \times 0.224951$$ $$BG^2 = 4321 + 446.3 = 4767.3$$ - Therefore: $$BG = \sqrt{4767.3} \approx 69.0 \text{ km}$$ 5. **Step iii) Bearing of G from B:** - Angle at B between north and BG is 4° to the east of north. - Bearing of G from B = 4° **Final answers:** - i) Bearing of B from F = 103° - ii) Distance BG = 69.0 km - iii) Bearing of G from B = 4°