Angles and Turns

The objectives of this section are to

Angles are an important building block in geometry and trigonometry as you will see later. In this unit you will see how turns are related to angles, how to measure them and how to work out their size in particular problems.

You will need to understand clearly what the terms such as turn, half turn, etc. mean in terms of angles. There are 360 ° in one complete turn, so the following are true.

You also need to refer to compass points: (north (N), south (S), east (E), west (W), northeast (NE), southeast (SE), southwest (SW) and northwest (NW).

1

What angle do you turn through if you turn

(a)

from NE to NW anticlockwise,

Show You can see that this is 90° (or turn).
(b)

from E to N clockwise?

Show This is a turn, i.e. 270°.

John is standing on a hill. The church is north of the point where he stands.

(a)

In what direction is he facing if he looks at:

(i)
the chimney,
(ii)
the bridge,
(iii)
the TV mast,
(iv)
the farm,
(v)
the oak tree?
(b)

What angle does John turn through if he turns clockwise from looking at:

(i)
the church to the farm, °
(ii)
the oak tree to the bridge, °
(iii)
the TV mast to the oak tree, °
(iv)
the bridge to the TV mast, °
(v)
the TV mast to the church? °
(c)

What would the angles be for question (b) if John turned anticlockwise instead of clockwise?

(i)
the church to the farm, °
(ii)
the oak tree to the bridge, °
(iii)
the TV mast to the oak tree, °
(iv)
the bridge to the TV mast, °
(v)
the TV mast to the church? °

In a game, you spin a pointer and let it stop.
What angle does the pointer turn through if it completes:

(a)
1 turn, °
(b)
2 turns, °
(c)
turn, °
(d)
turns, °
(e)
turns, °
(f)
turns? °

What angle do you turn through if you turn clockwise from facing:

(a)
N to E, °
(b)
W to NW, °
(c)
SE to NW, °
(d)
NE to N, °
(e)
W to NE, °
(f)
S to SW, °
(g)
S to SE, °
(h)
SE to SW, °
(i)
E to SW? °

What angle do you turn through if you turn anticlockwise from facing:

(a)
N to SW, °
(b)
S to SW, °
(c)
W to NW, °
(d)
E to S? °

In what direction will you be facing if you turn:

(a)

180° clockwise from NE,

(b)

180° anticlockwise from SE,

(c)

90° clockwise from SW,

(d)

45° clockwise from N,

(e)

225° clockwise from SW,

(f)

135° anticlockwise from N,

(g)

315° clockwise from SW?

Noravo stands on a low hill. The diagram below shows some of the things he can see. Using information from the diagram, answer the following questions.

(a)

What is NE of Noravo?

(b)

What is SE of Noravo?

(c)

Noravo turns from looking at the Old Fort to look at the ship. What angle does he turn through?

° or °
(d)

What angle does Noravo turn through if:

(i)

he turns clockwise from looking at the ship to the crane,

°
(ii)

he turns anticlockwise from looking at the radio mast to the factory,

°
(iii)

he turns anticlockwise from looking at the factory to the ship?

°
(e)

Noravo starts looking at the factory. What does he end up looking at if he turns:

(i)
135° clockwise,
(ii)
270° anticlockwise,
(iii)
225° clockwise,
(iv)
405° clockwise?

Use the diagram on the next page to answer these questions.

(a)

What is N of the shop?

(b)

What is W of the church?

(c)

What is E of the church?

(d)

What is E of Big Rock and NE of the shop?

(e)

What is SW of Big Rock?

(f)

In what direction should you walk from the beach to get to the tower?

(g)

In what direction should you walk from the beach to get to the church?

(h)

If you walk SE from the windmill, will you get to the tower?

The sketched map below shows towns and villages in west Jamaica.

(a)

What is east of Silver Spring?

(b)

What is north of Grange Hill?

(c)

What is SE of Grange Hill?

(d)

What is NW of Little London?

(e)

What is north east of Green Island and north west of Banbury?

(f)

What is north west of Little London and north of Sheffield?

The sails of a windmill complete one full turn every 40 seconds.

(a)

How long does it take the sails to turn through:

(i)
180° s
(ii)
90° s
(iii)
45° ? s
(b)

What angle do the sails turn through in:

(i)
30 seconds, °
(ii)
15 seconds, °
(iii)
25 seconds? °

The diagram shows the positions of Jason and Nadina. The arrow shows the direction of north.

Copy or trace the diagram.

Karen is west of Nadina and north of Jason. Mark Karen's position on your diagram.

Jenny is east of Jason and southeast of Nadina. Mark Jenny's position on your diagram.

(a)

Wendy is west of Jenny and southeast of Karen. Where is Wendy in relation to Nadina?

Wendy is of
(b)

Jai is north of Jason and south of Karen. Describe where he could be standing.

Anywhere on straight line joining position to .