lnf.cymru stimulus sheet · Maths · Year 7

Trwyn Eithin lighthouse: turns, directions and bearings

The lighthouse, the boats and the rocks on this sheet are invented. The facts about turns, compass points and bearings are real.

1. The lighthouse

Trwyn Eithin lighthouse stands on a rocky headland on the Welsh coast. Its lamp sends out one bright beam. The beam turns clockwise, the same way as the hands of a clock, and it makes 1 full turn every 12 seconds. Every night at 21:00 the keeper, Mared, starts the beam pointing North.

2. Turns and angles

Turn	Angle	What it looks like
Full turn	360°	Back to where you started
Three-quarter turn	270°	North round to West, clockwise
Half turn	180°	Facing the opposite way. A straight line.
Quarter turn	90°	A right angle. North to East, clockwise.

Types of angle

Name	Size
Acute	Less than 90°
Right angle	Exactly 90°
Obtuse	More than 90° and less than 180°
Straight line	Exactly 180°
Reflex	More than 180° and less than 360°

3. The 8 compass points

Going clockwise from North, each compass point is 45° further round.

Point	N	NE	E	SE	S	SW	W	NW
Name	North	North-east	East	South-east	South	South-west	West	North-west
Clockwise from N	0°	45°	90°	135°	180°	225°	270°	315°

4. Bearings

A bearing is an angle measured clockwise from North.
A bearing is always written with 3 digits: 40° is written 040°, and 5° is written 005°.
East is 090°, South is 180° and West is 270°.

How to measure a bearing with a protractor

1. Put the centre of the protractor on the lighthouse dot. 2. Line up the 0 line of the protractor with the North line. 3. Count round clockwise from 0 and read where the boat's line crosses the scale. 4. If the line is past South (more than 180°), measure the angle ANTICLOCKWISE from North instead, then take it away from 360°. Example: 50° anticlockwise from North is a bearing of 360 − 50 = 310°.

5. The map: boats near Trwyn Eithin tonight

The lines join the lighthouse to 4 boats. Angles do not change when a page is printed bigger or smaller, so you can measure them on any copy.

Boat	Name	Radio message to Mared
A	Seren	“Fishing for crab. Staying here until 23:00.”
B	Gwylan	“Heading home to the harbour.”
C	Morlo	“Anchored for the night.”
D	Dolffin	“Watching for seals. Engine is fine.”

6. Rocks to add to Mared’s chart

Rock	Bearing from the lighthouse
Craig Ddu	065°
Carreg Wen	150°
Y Gwastad	240°