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Sine Rule and Cosine Rule PowerPoint PPT Presentation

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:. a sin A. b sin B. c sin C. ==. C. b. The sides are labelled to match their opposite angles. a. A. B. c. The Sine Rule:.

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:

a

sinA

b

sinB

c

sinC

==

C

b

The sides are labelled to match their opposite angles

a

A

B

c

The Sine Rule:

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)

G

41º

76º

I

H

26 mm

Degree mode!!

• 5.53

• 0

B

53º

3 sig figs!!

62º

A

5 cm

C

3 sig figs!!

F

13 cm

28º

130º

D

E

• 6.36

• 0

C

47º

5 cm

θ

B

A

6 cm

3 sig figs!!

• 51.1

• 0.1

Q

6 km

P

27º

3.5 km

θ

R

• 57.7

• 0

D

8 m

θ

3 sig figs!!

F

70º

9.5 m

E

We use the Cosine Rule when:

Two sides and the INCLUDED angle (SAS)

OR

All three sides (SSS)

The Cosine Rule

A

c

b

B

C

a

B

C

(One side)2

=

(other side)2+(last side)2

-

2(other side)(last side)cos(angle of 1st side)

3 sig figs!!

• 3.38

• 0

3 sig figs!!

• 8.39

• 0

B

8.3 cm

72º

A

5.4 cm

C

3 sig figs!!

• 68.7

• 0

G

13 cm

11 cm

θ

I

H

12 cm

3 sig figs!!

• 112

• 0

F

10 cm

5 cm

D

7 cm

E

3 sig figs!!

• 104

• 0