11x1 t04 05 sine rule (2011)

Sine RuleA

B Ca

bc

Sine RuleA

B C

h

a

bc

Sine RuleA

B C

h

a

bc

sin

sin

h Bch c B

Sine RuleA

B C

h

a

bc

sin

sin

h Bch c B

sin

sin

h Cbh b C

Sine RuleA

B C

h

a

bc

sin

sin

h Bch c B

sin

sin

h Cbh b C

sin sin

sin sin

c B b Cc bC B

Sine RuleA

B C

h

a

bc

sin

sin

h Bch c B

sin

sin

h Cbh b C

sin sin

sin sin

c B b Cc bC B

In any ABC

sin sin sina b c

A B C

e.g. i H

Q

Lh

43 26

57 46

37.2

e.g. i H

Q

Lh

43 26

57 46

37.2

sin sinh qH Q

37.2sin57 46 sin 43 26

h

e.g. i H

Q

Lh

43 26

57 46

37.2

sin sinh qH Q

37.2sin57 46 sin 43 26

h

37.2sin57 46sin 43 26

h

45.8 units (to 1 dp)h

e.g. i H

Q

Lh

43 26

57 46

37.2

sin sinh qH Q

37.2sin57 46 sin 43 26

h

37.2sin57 46sin 43 26

h

45.8 units (to 1 dp)h ( )ii

F

Y

Z106 32

12.36

16.21

e.g. i H

Q

Lh

43 26

57 46

37.2

sin sinh qH Q

37.2sin57 46 sin 43 26

h

37.2sin57 46sin 43 26

h

45.8 units (to 1 dp)h ( )ii

F

Y

Z106 32

12.36

16.21

sin sinY Zy z

sin sin106 3212.36 16.21

Y

e.g. i H

Q

Lh

43 26

57 46

37.2

sin sinh qH Q

37.2sin57 46 sin 43 26

h

37.2sin57 46sin 43 26

h

45.8 units (to 1 dp)h ( )ii

F

Y

Z106 32

12.36

16.21

sin sinY Zy z

sin sin106 3212.36 16.21

Y

46 58Y

12.36sin106 32sin16.21

Y

Note: does your answer make sense?

Note: does your answer make sense?Check whether your answer might be obtuse, remember;

Note: does your answer make sense?Check whether your answer might be obtuse, remember;

angle sum = 180

Note: does your answer make sense?Check whether your answer might be obtuse, remember;

angle sum = 180

largest angle is opposite the largest side

Note: does your answer make sense?Check whether your answer might be obtuse, remember;

angle sum = 180

largest angle is opposite the largest side

A B

C

Note: does your answer make sense?Check whether your answer might be obtuse, remember;

angle sum = 180

largest angle is opposite the largest side

A B

Cd

circumcircle

Note: does your answer make sense?Check whether your answer might be obtuse, remember;

angle sum = 180

largest angle is opposite the largest side

A B

Cd

circumcircle

diametersin sin sin

a b cA B C

Area of a TriangleA

B Ca

bc

Area of a TriangleA

B C

h

a

bc

Area of a TriangleA

B C

h

a

bc

1Area2

ah

Area of a TriangleA

B C

h

a

bc

1Area2

ah sin

sin

h Cbh b C

Area of a TriangleA

B C

h

a

bc

1Area2

ah sin

sin

h Cbh b C

1Area sin2

ab C

Area of a TriangleA

B C

h

a

bc

1Area2

ah sin

sin

h Cbh b C

1Area sin2

ab C

In any ABC1Area sin21 sin21 sin2

ab C

bc A

ac B

Area of a TriangleA

B C

h

a

bc

1Area2

ah sin

sin

h Cbh b C

1Area sin2

ab C

In any ABC1Area sin21 sin21 sin2

ab C

bc A

ac B

e.g. M

F

D

60 15

9.21

6.37

Area of a TriangleA

B C

h

a

bc

1Area2

ah sin

sin

h Cbh b C

1Area sin2

ab C

In any ABC1Area sin21 sin21 sin2

ab C

bc A

ac B

e.g. M

F

D

60 15

9.21

6.37

1Area sin2

dm F

1 9.21 6.37 sin 60 152

Area of a TriangleA

B C

h

a

bc

1Area2

ah sin

sin

h Cbh b C

1Area sin2

ab C

In any ABC1Area sin21 sin21 sin2

ab C

bc A

ac B

e.g. M

F

D

60 15

9.21

6.37

1Area sin2

dm F

1 9.21 6.37 sin 60 152

225.47 units (to 2 dp)

Area of a TriangleA

B C

h

a

bc

1Area2

ah sin

sin

h Cbh b C

1Area sin2

ab C

In any ABC1Area sin21 sin21 sin2

ab C

bc A

ac B

e.g. M

F

D

60 15

9.21

6.37

1Area sin2

dm F

1 9.21 6.37 sin 60 152

225.47 units (to 2 dp)

Exercise 4H; 1a, 2b, 3a, 4, 8, 9, 10, 12, 14, 16, 18, 20, 22*