Given that Y is 20cm on a bearing of 300$^o$ from x, how far south of y is x?

Analyze the question: Y is 20 cm from X on a bearing of 300°. We need the distance X is south of Y, which is the north-south component of the displacement from X to Y.

Concept: A bearing is measured clockwise from North. A bearing of 300° lies in the north-west quadrant. Its angle from North is 360° − 300° = 60° towards the west.

• North component (how far north Y is of X) = 20 cos 60°
• West component = 20 sin 60°

Solution:

Northward distance = 20 × cos 60° = 20 × 0.5 = 10 cm

Y is 10 cm north of X, so X is 10 cm south of Y.

Check against the options: The answer is 10 cm, which is option A.

Tip: For bearings, the distance along the North-South line is d cos θ and along the East-West line is d sin θ, where θ is the acute angle from the North-South line. For 300°, use 360° − 300° = 60° from North. Always sketch a small compass diagram first.