Transcript Slide 1

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PLT Skills
LESSON OBJECTIVES
Always aim
high!
We are learning to:
- Finding connections between different words. (Which
PLT skills?)
- Accurately use trigonometry to calculate missing sides
and angles in right angled triangles. (Grade B)
Where are we in
our journey?
AUTHOR
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Real life
cross/curricular
links?
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BRAIN IN GEAR
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EXAMPLE
DITDIONA can be rearranged to make ADDITION
TASK
Work out the following Mathematical anagrams:
OATIR
Ratio
AVRELIAB
Variable
SENIVER
Inverse
EXTENSION
Develop your own Mathematical anagrams as above as a
creative thinker.
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STARTER
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TASK
1)Write 0.6 as 2) Write 912000 in 3) Write
a fraction
6
3
=
=
10
5
=
standard form
5
9.12 x 10
=
12
40
as a %
6
= 30%
20
4) Find 15% of $720
=
$108
5)Write 0.00134 in 6) Expand and simplify: 7) Value of: 8) Value of:
standard form
-3
= 1.34 x 10
EXTENSION
..
=
=
8(x - 3) - 5(x - 6)
8x - 24 – 5x + 30
3x + 6
Write 0.48 as a fraction
x = 0.484848…..
100x = 48.484848……
99x = 48
48
x=
99
0
=
372
1
=
4
32
5
2
Factorise the following:
x2 + 2x - 24 = ( x + 6)( x - 4 )
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TRIGONOMETRY
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Make sure your calculator is set to D or Deg not R or Rad
INTRODUCTION – USING YOUR CALCULATOR
Find the values, rounding the answers to 3s.f.
where appropriate.
(a) sin 54 (b) sin 26 (c) sin 90 (d) sin 0
= 0
= 0.809
= 0.438
= 1
(e) cos 54 (f) cos 26 (g) cos 90 (h) cos 0
= 1
= 0.588
= 0.899
= 0
(i) tan 54 (j) tan 26 (k) tan 89 (l) tan 0
= 0
= 1.38
= 0.488
= 57.3
5
(p)
(n)
6
cos
24
(o) 8 tan 44
(m) 4 sin 62
sin 72
= 3.53
= 5.48
= 7.73
= 5.26
5
4
(q) 8
(r) 9
(s) tan-1 7 (t) cos-1 8
cos 35
= 9.77
tan 18
= 27.7
SHIFT tan
= 29.7
SHIFT cos
= 51.3
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TRIGONOMETRY
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INTRODUCTION – LABELLING SIDES CORRECTLY
This is
opposite
the
angle.
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This is
opposite the
right-angle.

This is next to the angle.
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TRIGONOMETRY
INTRODUCTION – LABELLING SIDES CORRECTLY
Label the sides of the triangles below with opposite, adjacent and hypotenuse:
(b)
(d)
(a)
(c)
A
H
O
H
H
O O
A
A
A
(e)
O
(f)
A
H
A
O
H
O
A
(g)
H
(h)
A
H
O
O
H
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TRIGONOMETRY
INTRODUCTION
Some Old Hag Cracked All Her Teeth On Asparagus
SOH CAH TOA
o
s
H
A
o
C H
T A
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EXAMPLES
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TRIGONOMETRY
A
1) Work out the missing angles below:
(a)
H
O
(b)
A
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Worker
H
A
(c)
O
H
O
SUBSTITUTE
WRITELABEL
DOWNIN
THE
THE
THE
SIDES
FORMULA
VALUES SUBSTITUTE
WRITELABEL
DOWNIN
THE
THE
THE
SIDES
FORMULA
VALUES SUBSTITUTE
WRITELABEL
DOWNIN
THE
THE
THE
SIDES
FORMULA
VALUES
4
3
10
sin θ =
cos θ =
tan θ =
9
11
6
3
10
-1 4
θ = 74.2°(3s.f) θ = tan -1
θ = 59.0°(3s.f)
θ = sin 9 θ = 26.4°(3s.f) θ = cos-1
11
6
2) Work out the missing lengths below:
(a)
(b)
H
H
O
(c)
O
H
A
A
WRITE
DOWNTHE
THE
FORMULA
LABEL
SIDES
SUBSTITUTE
IN
THE
VALUES
b
sin 64 =
9
O
A
WRITE
DOWNTHE
THE
FORMULA
LABEL
SIDES
SUBSTITUTE
IN
THE
VALUES SUBSTITUTE
WRITE
DOWNTHE
THE
FORMULA
LABEL
SIDES
IN
THE
VALUES
b
cos 33 =
14
4
b = 9 x sin 64 b = 8.09cm(3s.f) b = 14 x cos 33 b = 11.7cm(3s.f) b =
b=
tan 46
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TRIGONOMETRY
TASK 1 (GRADE B) – FINDING MISSING ANGLES
(a)
(b)
H
O
(c)
H
(d)
O
A
A
A
Work out θ
Work out θ
(e)
H
(f)
A
O
Work out θ
Work out θ
2m
(h)
(g)
O
O
Work out θ
H
Work out θ
O
Work out θ
A
H
18m
Work out θ
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TRIGONOMETRY
TASK 2 (GRADE B) – FINDING MISSING SIDES
(a)
(b)
O
(c)
H
O
A
Find the value of x
(e)
H
A
Find the value of x
Find the value of x
(f)
A
Find the value of x
(g)
A
O
Find the value of x
(d)
H
A
H
Find the value of x
H
O
Find the value of x
(h) A
O
Find the value of x
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TRIGONOMETRY
TASK 3 (GRADE B) – TREASURE HUNT
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TRIGONOMETRY
TASK 4 (GRADE B) – TREASURE HUNT
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TRIGONOMETRY
TASK 5 (GRADE B) – BINGO
Draw a 3 x 3 grid as shown below:
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Place any nine numbers below into the grid (repeats forbidden)
Cos
20
10
Tan-1
Hyp
Sin
Adj
17
Sin-1
7/25
23/35
Cos-1
13/25
Opp
Tan
23/20
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TRIGONOMETRY
TASK 5 (GRADE B) – BINGO
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Name the trigonometry ratio used
to work out:
?
10cm
32o
Team
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Sin
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TRIGONOMETRY
TASK 5 (GRADE B) – BINGO
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What is the name of side with the ?
?
32o
Hyp
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TRIGONOMETRY
TASK 5 (GRADE B) – BINGO
Self
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Name the trigonometry ratio used
to work out:
Tan
10cm
32o
?
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TRIGONOMETRY
TASK 5 (GRADE B) – BINGO
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What is value of ?
Opposite = ? x sin 25
10cm
Opposite
25o
7cm
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10
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TRIGONOMETRY
TASK 5 (GRADE B) – BINGO
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What is the name of side with the ?
32o
?
Adj
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TRIGONOMETRY
TASK 5 (GRADE B) – BINGO
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Name the trigonometry ratio used
to work out:
?
15cm
10cm
Team
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Cos
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TRIGONOMETRY
TASK 5 (GRADE B) – BINGO
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What is value of ?
-1
x = cos ?
X
25cm
13cm
7cm
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13
25
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TRIGONOMETRY
TASK 5 (GRADE B) – BINGO
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Name the trigonometry ratio used
to work out:
x= ?
10
23
23cm
-1
10cm
x
Team
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Sin
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TRIGONOMETRY
TASK 5 (GRADE B) – BINGO
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What is value of ?
13cm
-1
x = sin ?
X
7cm
25cm
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7
25
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TRIGONOMETRY
TASK 5 (GRADE B) – BINGO
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What is the name of side with the ?
?
32o
Opp
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TRIGONOMETRY
TASK 5 (GRADE B) – BINGO
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What is value of ?
-1
x = tan
20cm
?
10
X
17cm
10cm
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17
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TRIGONOMETRY
TASK 5 (GRADE B) – BINGO
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Name the trigonometry ratio used
to work out:
x= ?
12cm
10
12
x
-1
10cm
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Tan
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TRIGONOMETRY
TASK 5 (GRADE B) – BINGO
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What is value of ?
32o
Opposite
Opposite = ? x sin 32
20cm
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20
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TRIGONOMETRY
TASK 5 (GRADE B) – BINGO
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What is ?:
x= ?
20
32
32cm
x
20cm
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-1
Cos
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TRIGONOMETRY
TASK 5 (GRADE B) – BINGO
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What is value of ?
-1
x = tan ?
35cm
23cm
X
20cm
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23
20
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TRIGONOMETRY
TASK 5 (GRADE B) – BINGO
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What is value of ?
-1
x = sin ?
35cm
23cm
X
20cm
Team
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23
35
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TRIGONOMETRY
EXTENSION 1 (GRADE B)
1)
2)
O
6cm
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Ox
θ
23°
10cm A
Opposite
Adjacent
tan θ = 6
10
-1 6
θ = tan 10
tan θ =
θ = 31.0°(3s.f)
100m A
Opposite
Adjacent
x
tan 23 =
100
tan θ =
x = 100 x tan 23
x = 42.4m(3s.f)
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TRIGONOMETRY
EXTENSION 2 (GRADE B)
1)
2)
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xA
43°
H
32m
x
39°
O
O
100m
100m
1m
Opposite
Hypotenuse
x
sin 39 =
32
sin θ =
x = 32 x sin 39
x = 20.1m(3s.f)
Height above
ground = 21.1m
Opposite
Adjacent
tan 43 = 100
x
100
x=
tan 43
tan θ =
x = 107m(3s.f)
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x
(b)
(c)
15cm
12cm
x
42°
8.6cm
H
A
Adjacent
cos θ =
Hypotenuse
4.3
cos 42 =
x
4.3
x=
cos 42
x = 5.79cm(3s.f)
(d)
20cm
74°
x
x = 7.42cm
H
A
32°
x
72°
H
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TRIGONOMETRY
EXTENSION 3 (GRADE B)
1)Find the side or angle marked x
(a)
Self
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74°
45cm
H
A
A
Adjacent
Adjacent
Adjacent
cos
θ
=
cos
θ
=
cos θ =
Hypotenuse
Hypotenuse
Hypotenuse
22.5
y
10
cos
74
=
cos 72 =
cos θ =
x
12
15 10
22.5
-1
x=
y = 12 x cos 72
θ = cos 15
cos 74
θ = 48.2°(3s.f)
y = 3.71cm(3s.f)
x = 81.6cm(3s.f)
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TRIGONOMETRY
MINI-PLENARY – ASSESSING UNDERSTANDING
H
O
A
Work out the values of both x and y
Adjacent
Hypotenuse
x
cos 36 =
7
cos θ =
x = 7 x cos 36
x = 5.66(3s.f)
Opposite
Hypotenuse
y
sin 36 =
7
sin θ =
y = 7 x sin 36
y = 4.11(3s.f)
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DISCOVERY
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LINK BACK TO OBJECTIVES
- Accurately use trigonometry to calculate
missing sides and angles in right angled
triangles.
What grade
are we
working at?
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TRIGONOMETRY
PLENARY ACTIVITY– EXAM QUESTION (GRADE B)
ABC and ACD are right-angled triangles. AD is parallel to BC.
AB = 12cm, BC = 5cm and AD = 33.8cm.
Calculate the size of angle ADC.
Opposite
sin x =
Pythagoras’ Theorem
D
Hypotenuse
to calculate y
2
x
H
33.8cm
O
13cm
y
C
5cm
A
12cm
B
2
2
y = 5 + 12
y 2 = 25 + 144
y 2 = 169
y = √169
y = 13cm
sin x =
13
33.8
-1
13
x = sin 33.8
x = 22.6°(3s.f)
What have you learnt?
Draw your brain
In your brain, write or draw everything you can remember about using the
trigonometry to calculate missing sides and angles in right angled triangles. It can
be a skill or a reflection, or something else that might be prominent in your brain.
Where are we
in our
journey?
What grade
are we
working at?
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Enterprise Skills SELF ASSESSMENT Which ones are you using?
Plenary Activity
How well do you understand the task?
.
I don’t
understand
I nearly
understand
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I fully
understand
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Enterprise Skills SELF ASSESSMENT Which ones are you using?
Plenary Activity
WWW (What Went Well)
EBI (Even Better If)
On your post it
notes…
Think about how you
can improve your
work.
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