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Trigonometry

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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. – PowerPoint PPT presentation

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Title: Trigonometry


1
Trigonometry
2
Describe what a bearing is.
3
Describe what a bearing is.
  • A bearing is a measurement of an angle from North
    in a clockwise direction.

4
Do you know how to write a vector?
5
Do you know how to write a vector?
  • A vector is written like this

6
An example of a vector.
3
-4
7
An example of a vector.
3
-4
Vector
8
Problems
9
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?
10
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
11
Solve using cosine
50 m
62
x
12
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.
13
(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

14
(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
15
(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
16
(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
17
(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
18
(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
19
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.
20
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
21
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
22
  • 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
23
  • 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
24
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.
25
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
26
Draw a diagram
h
38
60
1.7
27
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?
28
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
29
Draw a diagram
x
3.5
3.5
3.5
0.85
1.7
30
x
3.5
3.5
3.5
0.85
1.7
31
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?
32
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
33
Draw a diagram
45
30
50
z
x
y
34
x 40.1 m
45
30
50
z
x
y
35
Angle BAC is 32 degrees and AB and CB are 30 and
20 m resp. Find angle BCD
B
A
E
C
D
36
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
37
B
30
h
20
32
A
E
C
D
38
B
30
h
20
32
A
E
C
D
39
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.
40
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
41
Find x
70
20
120
x
42
Find y
40
50
y
43.7
120
h
43.7
43
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?
44
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
45
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
46
Originally the masses are hanging down 4 cm.
8 cm
x
y
47
Originally the masses are hanging down 4 cm.
4
x
y
48
Solve the equations by substitution
4
x
y
49
4
x
y
Height that it rises is 1 cm
50
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.
51
  • 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
52
  • 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
53
  • Use Pythagoras

x7
y
x
54
x7
y
x
55
x7
y
x
Lengths of sides are 8cm, 15cm and 17 cm
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