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Sine Rule and Cosine Rule

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```Sine Rule and Cosine
Rule
Clicker Practice
SOH/CAH/TOA can only be used for right-angled triangles.
The Sine Rule can be used for any triangle:
C
b
The sides are labelled to match
their opposite angles
A
The Sine Rule:
a
=
sinA
a
B
c
b
=
sinB
c
sinC
We use the Sine Rule when:
We have two angles and a side
OR
We have two sides and the non-included
angle (this is the ambiguous case)
Practice Together: find the length of
h in mm.
G
Degree
mode!!
76Вє
H
26 mm
I
41Вє
Find the length of a in cm.
B
53Вє
A
3 sig figs!!
62Вє
5.53
0
C
Find the length of f in cm.
3 sig figs!!
D
28Вє
F
130Вє
E
6.36
0
Practice Together: Find the
measure of angle ABC.
C
47Вє
Оё
A
6 cm
B
Find the measure of angle PRQ:
Q
P
27Вє
3.5 km
Оё
3 sig figs!!
R
51.1
0.1
Find the measure of angle EDF:
D
Оё
3 sig
figs!!
70Вє
E
F
57.7
0
We use the Cosine Rule when:
Two sides and the INCLUDED
angle (SAS)
OR
All three sides (SSS)
The Cosine Rule
Aп‚°
c
b
Bп‚°
B
Cп‚°
a
C
(One side)2
=
(other side)2+(last side)2
2(other side)(last side)cos(angle of 1st side)
Practice Together: Find the length
of side a
Find the length of side r in km:
3 sig figs!!
3.38
0
Find the length of AC in cm:
B
3 sig figs!!
72Вє
A
8.39
0
C
Practice Together: Find the
measure of the unknown angles
Find the measure of angle GHI
G
3 sig figs!!
Оё
I
H
12 cm
68.7
0
Find the measure of angle DEF:
3 sig figs!!
F
D
7 cm
E
112
0
Find the measure of the largest
angle of a triangle with sides 11cm,
13cm, and 19cm.
3 sig figs!!
104
0
```
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