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Trigonometry

Describe what a bearing is.

Describe what a bearing is.

- A bearing is a measurement of an angle from North

in a clockwise direction.

Do you know how to write a vector?

Do you know how to write a vector?

- A vector is written like this

An example of a vector.

3

-4

An example of a vector.

3

-4

Vector

Problems

A taut guy wire to the top of a transmission mast

is anchored in the same horizontal plane as the

foot of the mast. The wire is 50 m long and makes

an angle of 62 degrees with the horizontal. How

far is the lower end of the wire from the foot of

the mast?

Draw a diagram

- A taut guy wire to the top of a transmission mast

is anchored in the same horizontal plane as the

foot of the mast. The wire is 50 m long and makes

an angle of 62 degrees with the horizontal. How

far is the lower end of the wire from the foot of

the mast?

50 m

62

x

Solve using cosine

50 m

62

x

An aeroplane is flying at 300 km/hr. How far (a)

north (b) East of its starting-point is the

aeroplane after one hour if the direction of

flight is (i) North (ii)) N 40 degrees E (iii)

N 60 degrees E.

(i)

- An aeroplane is flying at 300 km/hr. How far (a)

north (b) East of its starting-point is the

aeroplane after one hour if the direction of

flight is (i) North (ii)) N 40 degrees E (iii)

N 60 degrees E.

- (a) 300 km
- (b) 0 km

(a) (ii)

- An aeroplane is flying at 300 km/hr. How far (a)

north (b) East of its starting-point is the

aeroplane after one hour if the direction of

flight is (i) North (ii)) N 40 degrees E (iii)

N 60 degrees E.

40

N

300

(a) (ii)

- An aeroplane is flying at 300 km/hr. How far (a)

north (b) East of its starting-point is the

aeroplane after one hour if the direction of

flight is (i) North (ii)) N 40 degrees E (iii)

N 60 degrees E.

40

N

300

(a) (iii)

- An aeroplane is flying at 300 km/hr. How far (a)

north (b) East of its starting-point is the

aeroplane after one hour if the direction of

flight is (i) North (ii)) N 40 degrees E (iii)

N 60 degrees E.

60

N

300

(b) (ii)

- An aeroplane is flying at 300 km/hr. How far (a)

north (b) East of its starting-point is the

aeroplane after one hour if the direction of

flight is (i) North (ii)) N 40 degrees E (iii)

N 60 degrees E.

E

40

300

(b) (iii)

- An aeroplane is flying at 300 km/hr. How far (a)

north (b) East of its starting-point is the

aeroplane after one hour if the direction of

flight is (i) North (ii)) N 40 degrees E (iii)

N 60 degrees E.

E

60

300

From a point 42 m above water-level at low tide

the angle of depression of a buoy in the water

was 57 degrees. At high tide the angle of

depression was 55 degrees. Find the horizontal

distance of the buoy from the viewer and the rise

of the tide.

Draw a diagram

- From a point 42 m above water-level at low tide

the angle of depression of a buoy in the water

was 57 degrees. At high tide the angle of

depression was 55 degrees. Find the horizontal

distance of the buoy from the viewer and the rise

of the tide.

57

42

x

Draw a diagram

- From a point 42 m above water-level at low tide

the angle of depression of a buoy in the water

was 57 degrees. At high tide the angle of

depression was 55 degrees. Find the horizontal

distance of the buoy from the viewer and the rise

of the tide.

57

33

42

x

- From a point 42 m above water-level at low tide

the angle of depression of a buoy in the water

was 57 degrees. At high tide the angle of

depression was 55 degrees. Find the horizontal

distance of the buoy from the viewer and the rise

of the tide.

57

33

42

x

- From a point 42 m above water-level at low tide

the angle of depression of a buoy in the water

was 57 degrees. At high tide the angle of

depression was 55 degrees. Find the horizontal

distance of the buoy from the viewer and the rise

of the tide.

27.3

55

x

42

Fred wishes to estimate the height of a building.

He steps out a distance of 60 m from the foot of

the building and finds the angle of elevation of

the top of the building is 38 degrees. Find the

height of the building if his eyes are at a

height of 1.7 m.

Draw a diagram

- Fred wishes to estimate the height of a building.

He steps out a distance of 60 m from the foot of

the building and finds the angle of elevation of

the top of the building is 38 degrees. Find the

height of the building if his eyes are at a

height of 1.7 m.

h

38

60

1.7

Draw a diagram

h

38

60

1.7

A step ladder with both sets of legs 3.5 m long

and hinged at the top is tied with a rope to

prevent the feet of the ladder being more than

1.7 m apart. What is the angle between the two

parts when the feet are fully apart?

Draw a diagram

- A step ladder with both sets of legs 3.5 m long

and hinged at the top is tied with a rope to

prevent the feet of the ladder being more than

1.7 m apart. What is the angle between the two

parts when the feet are fully apart?

3.5

3.5

1.7

Draw a diagram

x

3.5

3.5

3.5

0.85

1.7

x

3.5

3.5

3.5

0.85

1.7

From a point A on a straight and level road the

angle of elevation of the top of a tower at the

end of the road is 30 degrees. After walking

along the road to B the angle of elevation of the

top of the tower is 50 degrees. How long is AB if

the tower is 45 m high?

Draw a diagram

- From a point A on a straight and level road the

angle of elevation of the top of a tower at the

end of the road is 30 degrees. After walking

along the road to B the angle of elevation of the

top of the tower is 50 degrees. How long is AB if

the tower is 45 m high?

45

30

50

x

Draw a diagram

45

30

50

z

x

y

x 40.1 m

45

30

50

z

x

y

Angle BAC is 32 degrees and AB and CB are 30 and

20 m resp. Find angle BCD

B

A

E

C

D

Angle BAC is 32 degrees and AB and CB are 30 and

20 m resp. Find angle BCD

B

30

h

20

32

A

E

C

D

B

30

h

20

32

A

E

C

D

B

30

h

20

32

A

E

C

D

From the top of a building 120 m above the ground

the angles of depression of the top and bottom of

another building are 40 and 70 degrees

respectively. Find the distance apart of the

buildings and the height of the lower one.

Draw a diagram

- From the top of a building 120 m above the ground

the angles of depression of the top and bottom of

another building are 40 and 70 degrees

respectively. Find the distance apart of the

buildings and the height of the lower one.

70

40

120

h

x

Find x

70

20

120

x

Find y

40

50

y

43.7

120

h

43.7

Two small pulleys are placed 8 cm apart in a

horizontal line and an inextensible string of

length 16 cm is placed over the pulleys. Equal

masses hang symmetrically at each end of the

string and the middle point is pulled down

vertically until it is in line with the masses.

How far does each mass rise?

Draw a diagram

- Two small pulleys are placed 8 cm apart in a

horizontal line and an inextensible string of

length 16 cm is placed over the pulleys. Equal

masses hang symmetrically at each end of the

string and the middle point is pulled down

vertically until it is in line with the masses.

How far does each mass rise?

8 cm

x

y

Originally the masses are hanging down 4 cm.

- Two small pulleys are placed 8 cm apart in a

horizontal line and an inextensible string of

length 16 cm is placed over the pulleys. Equal

masses hang symmetrically at each end of the

string and the middle point is pulled down

vertically until it is in line with the masses.

How far does each mass rise?

8 cm

x

y

Originally the masses are hanging down 4 cm.

8 cm

x

y

Originally the masses are hanging down 4 cm.

4

x

y

Solve the equations by substitution

4

x

y

4

x

y

Height that it rises is 1 cm

In a right-angled triangle, one of the sides

including the right angle is 7 cm longer than the

other. If the perimeter is 40 cm, find the

lengths of the three sides.

- In a right-angled triangle, one of the sides

including the right angle is 7 cm longer than the

other. If the perimeter is 40 cm, find the

lengths of the three sides.

x7

y

x

- In a right-angled triangle, one of the sides

including the right angle is 7 cm longer than the

other. If the perimeter is 40 cm, find the

lengths of the three sides.

x7

y

x

- Use Pythagoras

x7

y

x

x7

y

x

x7

y

x

Lengths of sides are 8cm, 15cm and 17 cm