Sine Rule and Cosine Sine Rule and Cosine RuleRule
Clicker PracticeClicker Practice
SOH/CAH/TOA can only be used for right-angled triangles.SOH/CAH/TOA can only be used for right-angled triangles.
The Sine Rule can be used for The Sine Rule can be used for anyany triangle: triangle:
A B
C
ab
c
The sides are labelled to match their opposite angles
asinA
bsinB
csinC= =The Sine Rule:
We use the Sine Rule when: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 Practice Together: find the length of h in mm.h in mm.
G
H
I
41º
76º26 mm
Degree mode!!
Find the length of a in cm.Find the length of a in cm.
5.535.5300
A
B
C
62º
53º
5 cm
3 sig figs!!
Find the length of f in cm.Find the length of f in cm.
6.366.3600D
E
F
28º 130º
13 cm
3 sig figs!!
Practice Together: Find the Practice Together: Find the measure of angle ABC.measure of angle ABC.
47º
6 cm
5 cm
A B
C
θ
Find the measure of angle PRQ:Find the measure of angle PRQ:
51.151.10.10.1
27º
6 km
3.5 km
3 sig figs!!
P
Q
R
θ
Find the measure of angle EDF:Find the measure of angle EDF:
57.757.700
8 m
70º9.
5 m
D
E
Fθ
3 sig figs!!
We use the Cosine Rule when:We use the Cosine Rule when:
Two sides and the INCLUDED angle (SAS)
OR
All three sides (SSS)
The Cosine RuleThe Cosine Rule
CB
c
a
b
B
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 Practice Together: Find the length of side aof side a
Find the length of side r in km:Find the length of side r in km:
3.383.3800
3 sig figs!!
Find the length of AC in cm: Find the length of AC in cm:
8.398.3900
3 sig figs!!
A
B
C
72º
5.4 cm
8.3 cm
Practice Together: Find the Practice Together: Find the measure of the unknown anglesmeasure of the unknown angles
Find the measure of angle GHIFind the measure of angle GHI
68.768.700
G
H
Iθ12 cm
11 c
m
13 cm
3 sig figs!!
Find the measure of angle DEF:Find the measure of angle DEF:
11211200
3 sig figs!!
DE
F
10 cm
7 cm5 c
m
Find the measure of the largest Find the measure of the largest angle of a triangle with sides 11cm, angle of a triangle with sides 11cm,
13cm, and 19cm.13cm, and 19cm.
10410400
3 sig figs!!