Final answer:
A diagram can be drawn showing Manchester 170km north of Worcester and Cambridge 230km east of Worcester. Using trigonometry, the bearing of Manchester from Cambridge is calculated to be approximately 323.13°.
Step-by-step explanation:
To represent the described flight path and find the bearing of Manchester from Cambridge, we can draw a diagram with a coordinate system where north is along the positive y-axis and east is along the positive x-axis. Label Worcester as the origin (0,0), Manchester at (0,170) because it is 170km north of Worcester, and Cambridge at (230,0) since it is 230km east of Worcester.
To find the bearing from Cambridge to Manchester, we need to calculate the angle between the north directional line from Cambridge (which is our reference line for bearing) and the line connecting Cambridge to Manchester. Using the distance between Manchester and Worcester as the opposite side of a right triangle, and the distance between Worcester and Cambridge as the adjacent side, we use the arctangent function to find the angle.
Loading the bearing, we have:
- Let M represent Manchester and C represent Cambridge.
- Draw a line from C to M to form a right-angled triangle with the north-south line through Worcester (W).
- The angle θ between the north line and CM can be found using the inverse tangent function, tan-1(OW/OC) = tan-1(170/230).
- Calculate θ: θ ≈ tan-1(170/230) ≈ 36.87°.
- The bearing from C to M is thus 360° - 36.87° = 323.13°.
This bearing tells us that from Cambridge, Manchester lies at 323.13° clockwise from north.