Subjects geometry

Three Figure Bearings

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1. **State the problem**: We need to find the three-figure bearings from the centre to Town A and Town C based on given angles. 2. **Understand bearings**: Bearings are measured clockwise from the north direction, and are expressed as three digits. 3. **Calculate bearing to Town A from centre**: - The ray from centre to Town A is given as 35° east of north. - Bearing is measured clockwise from north, so bearing to Town A is simply $35^\circ$. - Write as a three-figure bearing: $035^\circ$. 4. **Calculate bearing to Town C from centre**: - The angle from Town A to Town B is 56°, so the bearing to Town B from centre is $35^\circ + 56^\circ = 91^\circ$. - The angle from Town B to Town C is 120°, so the bearing from centre to Town C is $91^\circ + 120^\circ = 211^\circ$. - This is already a three-figure bearing. 5. **Final answers:** - (a) Bearing to Town A from centre = $035^\circ$ - (b) Bearing to Town C from centre = $211^\circ$