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!!