A ship sails x km due east to a point E and continues x km due north to F. Find the bearing the bearing of f from the starting point.

Analyze the question: A ship starts at a point (call it O), sails x km due east to E, then x km due north to F. We need the bearing of F from O.

Concept: A bearing is measured clockwise from North, written as three digits. For the bearing of F from O, we stand at O and measure the angle from the North line to the line OF.

Solution:

1. Draw O at the origin. E is x km directly east of O. F is x km directly north of E.
2. Triangle OEF has a right angle at E, with OE = EF = x. So it is an isosceles right triangle, and the angles at O and F are each 45°.
3. Check with tan: the angle between OF and the East line is tan θ = EF/OE = x/x = 1, so θ = 45°.
4. The bearing is measured from North. Since OF lies 45° north of East, it is 45° from East toward North. East is 090°, so the bearing is 090° − 45° = 045°.

So F is on a line at 45° clockwise from North, which is north-east of O.

Answer: 045°, which is option A.

Tip: When a ship goes equal distances east and north, the bearing is always 045° (north-east). Equal distances east and south give 135°. Equal distances west and south give 225°. Equal distances west and north give 315°. Always sketch a small diagram and measure clockwise from North.