Direction Sense: Turns, Distances and the Right Triangle

Direction-sense questions describe a person walking, turning and walking again, then ask where they end up or how far from the start. A simple sketch solves nearly all of them.

The four directions

Draw a cross with North at the top, South at the bottom, East on the right and West on the left.

Turning left and right

If you face a direction and turn:

Facing	Turn right	Turn left
North	East	West
East	South	North
South	West	East
West	North	South

Sketch the path as you read.

Example 1: distance

A man walks 3 km north, then 4 km east. How far is he from the start?

The path forms a right triangle with sides 3 and 4. The straight-line distance is the hypotenuse:

√(3² + 4²) = √25 = 5 km.

Pythagorean triples

Memorise these triples, which appear often:

Sides	Hypotenuse
3, 4	5
5, 12	13
8, 15	17
7, 24	25
20, 21	29

Multiples work too: 6, 8, 10 and 9, 12, 15.

Example 2: final direction

A person faces north, turns right, walks 5 km, turns right again and walks 3 km. Which direction is he facing?

• Facing north, right turn = east.
• Facing east, right turn = south.

He faces south.

Example 3: position relative to the start

Ram walks 10 m south, then 20 m west, then 10 m north. Where is he relative to the start?

• South 10 then north 10 cancel out.
• He is 20 m west of the start.

Tips

1. Draw a fresh diagram each time.
2. Mark the start point.
3. Cancel opposite moves to simplify.
4. Use the triples to find distances quickly.

Shadow questions

Some questions use shadows. In the morning, the sun is in the east, so shadows fall towards the west. In the evening, the sun is in the west, so shadows fall towards the east.

Practice

Direction sense can be practised quickly. A few sketches daily make the method automatic.

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