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Stage 5 Trig (+ Pythag) SACHS
Contributed by: Shanahan
Identify the next line of working:
5
12
x
122 = x2 + 52
x2 = 52 + 122
?
c2 = a2 + b2
52= x2 + 122
Identify the next line of working:
5
12
x
x2 = 169
?
x2 = 52 + 122
c2 = a2 + b2
x2 = 25
x2 = 144
Identify the next line of working:
5
12
x
x2 = 169
x2 = 52 + 122
c2 = a2 + b2
x = √169
?
x2 = √169
Identify the next line of working:
5
12
x
x2 = 169
x2 = 52 + 122
c2 = a2 + b2
x = 13
?
x = √169
x = 169
Identify the next line of working:
x
7
15
72 = x2 + 152
152 = x2 + 72
?
c2 = a2 + b2
x2= 72 + 122
Identify the next line of working:
x
7
15
225 = x2
225 = x2 + 49
?
152 = x2 + 72
c2 = a2 + b2
x2= 225 + 49
Identify the next line of working:
x
7
15
What is the opposite operation?
– 49
?
225 = x2 + 49
152 = x2 + 72
c2 = a2 + b2
+ 49
Identify the next line of working:
x
7
15
176 = x2
?
225 = x2 + 49
-49
152 = x2 + 72
c2 = a2 + b2
176 = x2 + 49
Identify the next line of working:
x
7
15
176 = x2
225 = x2 + 49
-49
152 = x2 + 72
x = √176
?
c2 = a2 + b2
x2 = √176
Identify the next line of working:
x
7
15
176 = x2
225 = x2 + 49
-49
152 = x2 + 72
x = 13.3
?
x = √176
c2 = a2 + b2
x = 13.2
Understand the working:
50o
x
12
(Use the opposite operation to remove ÷12)
(Go to your calculator)
x
Identify the next line of working:
tan 34 = 5/x
5
34o
cos 34 = x/5
tan 34 = x/5
?
cos 34 = 5/x
x
Identify the next line of working:
5
34o
x × tan 34 = 5
5 × tan 34 = x
?
tan 34 = 5/x
x
Identify the next line of working:
5
34o
5 × tan 34 = x
x = 3.4
?
x = 3.3
Identify the next line of working:
tan 25 = 32/x
32
25o
x
tan 25 = x/32
cos 25 = x/32
?
cos 25 = 32/x
Identify the next line of working:
cos 25 = 32/x
32
25o
x
cos 25 /32 = x
32 × cos 25 = x
?
Identify the next line of working:
32
25o
x
x = 29.1
32 × cos 25 = x
x = 29.0
?
Understand the working:
x
62o
12
(Use the opposite operate to remove x tan 62)
(Use the opposite operation to remove ÷x)
(Go to your calculator)
Identify the next line of working:
cos 42 = x/58
58
x
42o
sin 43 = x/58
cos 42 = 58/x
?
sin 42 = 58/x
Identify the next line of working:
cos 42 = x/58
58
x
42o
58 × cos 43 = x
x × cos 42 = 58
?
Identify the next line of working:
58
x
42o
x = 58 / cos 42
?
x = 58 ×cos 42
Identify the next line of working:
58
x
42o
x = 78.0
?
x = 78.1
18
Identify the next line of working:
sin 66 = x/18
x
66o
cos 66 = x/18
sin 66 = 18/x
?
cos 66 = 18/x
18
Identify the next line of working:
sin 66 = x/18
x
66o
x = sin 66/18
x × sin 66 = 18
?
18
Identify the next line of working:
x = 18 × sin 66
x
66o
x = sin 66/18
x = 18 / sin 66
?
18
Identify the next line of working:
x
66o
x = 19.7
?
x = 19.8
Understand the working:
34
θo
21
(Use the opposite operation to remove cos)
(Go to your calculator)
25
Identify the next line of working:
tan θ = 16/25
16
θo
cos θ = 25/16
tan θ = 25/16
?
cos θ = 16/25
25
Identify the next line of working:
16
θo
θ = tan–1 25/16
?
θ = tan 16/25
25
Identify the next line of working:
16
θo
θ = 57.4
?
θ = 57.3
9
Identify the next line of working:
sin θ = 17/9
17
θo
cos θ = 17/9
sin θ = 9/17
?
cos θ = 9/17
9
Identify the next line of working:
17
θo
θ = sin–1 9/17
?
θ = sin 17/9
9
Identify the next line of working:
17
θo
θ = 32.0
?
θ = 31.9
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