**Sine and Cosine Rule**

Example

Example

Solving triangle problems

**Use sine and cosine rule to solve problems in non-right triangles.**

9 cm

12 cm

63

o

A

B

C

Find the angle ABC.

Starter

9 cm

12 cm

63

o

A

B

C

Find the angle ABC.

BC = 9 + 12 - 2(9)(12)Cos63

BC = 81 + 144 - 216Cos63

BC = 126.9380521

BC = 126.9380521 = 11.3 cm

2

2

2

2

2

Sin ABC 9

Sin 63 11.266...

=

9

11.266...

Sin ABC = x Sin 63

Sin ABC = 0.711750004

ABC = Sin 0.71175004 = 45.4

-1

o

15 cm

6 cm

98

o

A

B

C

Find the length BC.

Solving triangle problems

15 cm

6 cm

98

o

A

B

C

Find the length BC.

Sin BCA 6

Sin 98 15

=

Sin BCA = 0.4 x Sin 98

Sin BCA = 0.396107227

BCA = Sin 0.396107227 = 23.33504691

-1

o

So angle BAC = 180 - 98 - 23.335... = 58.66495309

o

BC Sin 58.66495309

15 Sin 98

=

BC = x 15

Sin 58.66495309

Sin 98

BC = 12.9 cm

A car travels 17 km from point A on a bearing of 040 to point B. The car then travels 25 km on a bearing of 072 to point C. Find the bearing and distance of C from A.

o

o

Example

A car travels 17 km from point A on a bearing of 040 to point B. The car then travels 25 km on a bearing of 072 to point C. Find the bearing and distance of C from A.

o

o

140

148

AC = 17 + 25 - 2(17)(25)Cos148

AC = 1634.840882

AC = 1634.840882 = 40.4 km

Sin BAC 25

Sin 148 40.433...

=

Sin BAC = x Sin 148

Sin BAC = 0.327651357

BAC = Sin 0.327651357 = 19.1

Bearing = 40 + 19.1 = 59.1

25

40.433...

2

2

2

2

o

o

Activity

Complete the worksheet about the Sine and Cosine rule.

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