3. 18 May 201518 May 2015 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
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Learning IntentionLearning Intention Success CriteriaSuccess Criteria
2.2. Work out Tan Ratio.Work out Tan Ratio.
1. To identify the
hypotenuse, opposite and
adjacent sides in a right
angled triangle.
Angles & TrianglesAngles & Triangles
1.1. Understand the termsUnderstand the terms
hypotenuse, opposite andhypotenuse, opposite and
adjacent in right angledadjacent in right angled
triangle.triangle.
9. www.mathsrevision.com
TrigonometryTrigonometry
Tan 25Tan 25°° 0.4660.466
Tan 26Tan 26°° 0.4880.488
Tan 27Tan 27°° 0.5100.510
Tan 28Tan 28°° 0.5320.532
Tan 29Tan 29°° 0.5540.554
Tan 30Tan 30°° 0.5770.577
Tan 31Tan 31°° 0.6010.601
Tan 32Tan 32°° 0.6250.625
Tan 33Tan 33°° 0.6490.649
Tan 34Tan 34°° 0.6750.675
Tan 30° = 0.577
Accurate to
3 decimal places!
The ancient Greeks
discovered this and
repeated this for
all possible angles.
S3
Credit
20. 18 May 201518 May 2015 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
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Learning IntentionLearning Intention Success CriteriaSuccess Criteria
2.2. Use tan of an angle to solveUse tan of an angle to solve
problems.problems.
1. To use tan of the angle to
solve problems.
Angles & TrianglesAngles & Triangles
1.1. Write down tan ratio.Write down tan ratio.
28. 18 May 201518 May 2015 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
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Learning IntentionLearning Intention Success CriteriaSuccess Criteria
2.2. Use tan of an angle to solveUse tan of an angle to solve
REAL LIFE problems.REAL LIFE problems.
1. To use tan of the angle to
solve REAL LIFE problems.
Angles & TrianglesAngles & Triangles
1.1. Write down tan ratio.Write down tan ratio.
29. www.mathsrevision.com
TrigonometryTrigonometryS3
Credit
SO
H CA
H TO
A
18 May 201518 May 2015 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Use the tan ratio to find the height h of the tree
to 2 decimal places.
47o
8m
rod
o opp h
tan 47 = =
adj 8
o h
tan 47 =
8
o
h = 8× tan 47
h = 8.58m
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TrigonometryTrigonometryS3
Credit
6o
18 May 2015
Compiled by Mr. Lafferty Maths
Dept.
Aeroplane
a = 15
c
LennoxtownAirport
Q1.Q1. An aeroplane is preparing to land at Glasgow Airport.An aeroplane is preparing to land at Glasgow Airport.
It is over Lennoxtown at present which is 15km fromIt is over Lennoxtown at present which is 15km from
the airport. The angle of descent is 6the airport. The angle of descent is 6oo
..
What is the height of the plane ?What is the height of the plane ?
Example 2Example 2
o h
tan 6 =
15
o
h = 15× tan 6
h = 1.58km
SO
H CA
H TO
A
33. 18 May 201518 May 2015 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
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Learning IntentionLearning Intention Success CriteriaSuccess Criteria
2.2. Use tan of an angle to solveUse tan of an angle to solve
find adjacent length.find adjacent length.
1. To use tan of the angle to
find adjacent length.
Angles & TrianglesAngles & Triangles
1.1. Write down tan ratio.Write down tan ratio.
34. www.mathsrevision.com
TrigonometryTrigonometryS3
Credit
18 May 201518 May 2015 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Use the tan ratio to calculate how far the ladder
is away from the building.
45o
12m
ladder
o opp 12
tan 45 = =
adj d
o
12
d =
tan 45
d = 12m
d m
SO
H CA
H TO
A
35. www.mathsrevision.com
TrigonometryTrigonometryS3
Credit
6o
18 May 201518 May 2015 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Aeroplane
a = 1.58 km
LennoxtownAirport
Q1. An aeroplane is preparing to land at Glasgow Airport. It is over
Lennoxtown at present. It is at a height of 1.58 km above the ground. It
‘s angle of descent is 6o
.
How far is it from the airport to Lennoxtown?
Example 2Example 2
o 1.58
tan 6 =
d
o
1.58
d =
tan 6
d = 15 km
SO
H CA
H TO
A
38. 18 May 201518 May 2015 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
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Learning IntentionLearning Intention Success CriteriaSuccess Criteria
2.2. Use tan ratio to find an angle.Use tan ratio to find an angle.
1. To show how to find an
angle using tan ratio.
Angles & TrianglesAngles & Triangles
1.1. Write down tan ratio.Write down tan ratio.
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TrigonometryTrigonometryS3
Credit
18 May 201518 May 2015 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Use the tan ratio to calculate the angle that the
support wire makes with the ground.
xo
11m
o opp 11
tan x = =
adj 4
11
4
÷
o -1
x = tan
o o
x = 70
4 m
SO
H CA
H TO
A
40. www.mathsrevision.com
TrigonometryTrigonometryS3
Credit
18 May 201518 May 2015 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Use the tan ratio to find the angle of take-off.
xo
88m
o opp 88
tan x = =
adj 500
o
tan x = 0.176
o -1 o
x = tan (0.176) = 10
500 m
SO
H CA
H TO
A
43. 18 May 201518 May 2015 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
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Learning IntentionLearning Intention Success CriteriaSuccess Criteria
2.2. Use sine ratio to find anUse sine ratio to find an
angle.angle.
1. Definite the sine ratio and
show how to find an angle
using this ratio.
Angles & TrianglesAngles & Triangles
1.1. Write down sine ratio.Write down sine ratio.
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Starter QuestionsStarter Questions
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1 2 3
1. Explain why we can simply pick out Q
the 5 figure summary for the data
19, 15, 11, 22, 9, 12, 11
2. Show that the original price of a car is £9000
If it cos
, Q and Q
then find
ts £8100 after a discount of 10%
3. Alorry is travelling at 40mph.
It has travelled 60 miles.
How long has it taken to travel 60 miles.
S3
Credit
52. 18 May 201518 May 2015 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
www.mathsrevision.com
Learning IntentionLearning Intention Success CriteriaSuccess Criteria
2.2. Use sine ratio to solveUse sine ratio to solve
REAL-LIFE problems.REAL-LIFE problems.
1. To show how to use the
sine ratio to solve
REAL-LIFE problems.
Angles & TrianglesAngles & Triangles
1.1. Write down sine ratio.Write down sine ratio.
53. www.mathsrevision.com
TrigonometryTrigonometryS3
Credit
SO
H CA
H TO
A
18 May 201518 May 2015 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
The support rope is 11.7m long. The angle between
the rope and ground is 70o
. Use the sine ratio to
calculate the height of the flag pole.
70o
h
o opp h
sin 70 = =
hyp 11.7
h × o
= 11.7 sin70
h = 11m
11.7m
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TrigonometryTrigonometryS3
Credit
SO
H CA
H TO
A
18 May 201518 May 2015 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Use the sine ratio to find the angle of the ramp.
xo
10m
o opp 10
sin x = =
hyp 20
o 10
sin x =
20
÷
o -1 o10
x = sin = 30
20
20 m
57. 18 May 201518 May 2015 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
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Learning IntentionLearning Intention Success CriteriaSuccess Criteria
2.2. Use sine ratio to find theUse sine ratio to find the
hypotenuse.hypotenuse.
1. To show how to calculate
the hypotenuse using the
sine ratio.
Angles & TrianglesAngles & Triangles
1.1. Write down sine ratio.Write down sine ratio.
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Starter QuestionsStarter Questions
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1 3
1. Explain why we can simply pick out Q
then find the 5 figure summary for the data
9, 5, 11, 2, 9, 2
2. Find the original price of a football
If it costs £20 after a discoun
and Q
t of 80%
3. Alorry is travelling at 50mph.
It has travelled 75 miles.
Show that the time taken is 1hr 30 mins.
S3
Credit
61. 18 May 201518 May 2015 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
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Learning IntentionLearning Intention Success CriteriaSuccess Criteria
2.2. Use cosine ratio to find aUse cosine ratio to find a
length or angle.length or angle.
1. Definite the cosine ratio
and show how to find an
length or angle using this
ratio.
Angles & TrianglesAngles & Triangles
1.1. Write down cosine ratio.Write down cosine ratio.
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The Three RatiosThe Three Ratios
Cosine
Sine
Tangent
Sine
Sine
Tangent
Cosine
Cosine
Sine
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S3
Credit
opposite
opposite opposite
adjacent
adjacent
adjacent
hypotenuse
hypotenuse
hypotenuse