1. Sine Rule
A
c b
B a C

2. Sine Rule
A
c b
h
B a C

3. Sine Rule
A h
 sin B
c
c h  c sin B
h b
B a C

4. Sine Rule
A h h
 sin B  sin C
c b
c h  c sin B h  b sin C
h b
B a C

5. Sine Rule
A h h
 sin B  sin C
c b
c h  c sin B h  b sin C
h b
 c sin B  b sin C
B C c b
a 
sin C sin B

6. Sine Rule
A h h
 sin B  sin C
c b
c h  c sin B h  b sin C
h b
 c sin B  b sin C
B C c b
a 
sin C sin B
In any ABC
a b c
 
sin A sin B sin C

7. e.g.  i  H
57 46
37.2
Q 43 26

h
L

8. e.g.  i  H
h q

sin H sin Q
57 46 h 37.2

37.2 sin 57 46 sin 43 26

Q 43 26

h
L

9. e.g.  i  H
h q

sin H sin Q
57 46 h 37.2

37.2 sin 57 46 sin 43 26

Q 43 26

37.2sin 57 46
h
h sin 43 26
L
h  45.8 units (to 1 dp)

10. e.g.  i  H
h q

sin H sin Q
57 46 h 37.2

37.2 sin 57 46 sin 43 26

Q 43 26

37.2sin 57 46
h
h sin 43 26
L
h  45.8 units (to 1 dp)
(ii )
F
16.21
12.36
Y
10632
Z

11. e.g.  i  H
h q

sin H sin Q
57 46 h 37.2

37.2 sin 57 46 sin 43 26

Q 43 26

37.2sin 57 46
h
h sin 43 26
L
h  45.8 units (to 1 dp)
(ii )
sin Y sin Z

F y z
16.21 sin Y sin10632

12.36 12.36 16.21
Y
10632
Z

12. e.g.  i  H
h q

sin H sin Q
57 46 h 37.2

37.2 sin 57 46 sin 43 26

Q 43 26

37.2sin 57 46
h
h sin 43 26
L
h  45.8 units (to 1 dp)
(ii )
sin Y sin Z

F y z
16.21 sin Y sin10632

12.36 12.36 16.21
Y 12.36sin10632
10632 sin Y 
16.21
Z
Y  4658

13. Note: does your answer make sense?

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

15. Note: does your answer make sense?
Check whether your answer might be obtuse, remember;
 angle sum  = 180

16. Note: does your answer make sense?
Check whether your answer might be obtuse, remember;
 angle sum  = 180
 largest angle is opposite the largest side

17. 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

18. 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
d C
circumcircle

19. 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
d C
a b c
   diameter
sin A sin B sin C
circumcircle

20. Area of a Triangle
A
c b
B a C

21. Area of a Triangle
A
c b
h
B a C

22. Area of a Triangle
A 1
Area  ah
2
c b
h
B a C

23. Area of a Triangle
A h
1  sin C
Area  ah b
2
c b h  b sin C
h
B a C

24. Area of a Triangle
A h
1  sin C
Area  ah b
2
1 h  b sin C
c
h b  Area  ab sin C
2
B a C

25. Area of a Triangle
A h
1  sin C
Area  ah b
2
1 h  b sin C
c
h b  Area  ab sin C
2
B C In any ABC
a
1
Area  ab sin C
2
1
 bc sin A
2
1
 ac sin B
2

26. Area of a Triangle
A h
1  sin C
Area  ah b
2
1 h  b sin C
c
h b  Area  ab sin C
2
B C In any ABC
a
e.g. M 1
Area  ab sin C
9.21 2
1
F 60 15
  bc sin A
2
6.37 1
D  ac sin B
2

27. Area of a Triangle
A h
1  sin C
Area  ah b
2
1 h  b sin C
c
h b  Area  ab sin C
2
B C In any ABC
a
e.g. M 1
1 Area  ab sin C
9.21 Area  dm sin F 2
2
1 1
F 60 15

  9.21 6.37  sin 6015  bc sin A
2 2
6.37 1
D  ac sin B
2

28. Area of a Triangle
A h
1  sin C
Area  ah b
2
1 h  b sin C
c
h b  Area  ab sin C
2
B C In any ABC
a
e.g. M 1
1 Area  ab sin C
9.21 Area  dm sin F 2
2
1 1
F 60 15

  9.21 6.37  sin 6015  bc sin A
2 2
6.37  25.47 units 2 (to 2 dp) 1
D  ac sin B
2

29. Area of a Triangle A h
1  sin C
Area  ah b
2
1 h  b sin C
c
h b  Area  ab sin C
2
B C In any ABC
a
e.g. M 1
1 Area  ab sin C
9.21 Area  dm sin F 2
2
1 1
F 60 15

  9.21 6.37  sin 6015  bc sin A
2 2
6.37  25.47 units 2 (to 2 dp) 1
D  ac sin B
2
Exercise 4H; 1a, 2b, 3a, 4, 8, 9, 10, 12, 14, 16, 18, 20, 22*