Points X and Y are 20km North and 9km East of point O, respectively. What is the bearing of Y from X? Correct to the nearest degree.

Analyze the question: O is the origin. X is 20 km North of O, so X = (0, 20) taking East as x and North as y. Y is 9 km East of O, so Y = (9, 0). We need the bearing of Y from X, which is the angle measured clockwise from North at X to the line XY.

Concept: A bearing is measured clockwise from North, written as three digits. Using the right-angled triangle XOY, with the right angle at O, we find the acute angle at X and then relate it to the bearing.

Solution:

1. In triangle XOY: XO = 20 km (vertical), OY = 9 km (horizontal).
2. The angle at X between the line XO (pointing South from X) and XY is: tan θ = OY / XO = 9/20 = 0.45 θ = tan⁻¹(0.45) ≈ 24.2° ≈ 24°
3. This angle θ is measured from the South direction at X. From X, Y lies to the south and east (down and to the right).
4. Bearing from North, clockwise: going East is 90°, South is 180°. Y is between East and South, 24° away from South toward East: Bearing = 180° − 24° = 156°

Check: Y is south-east of X, so the bearing must be between 90° and 180°. 156° fits, and 24° (option A) would wrongly point north-east.

Answer: D (156°)

Tip: For a bearing "of B from A", stand at A and draw a North line there. Then measure clockwise to the line towards B. Always sketch it first. Check which quadrant the answer falls in (SE means between 090° and 180°) to eliminate options quickly.