1. Cosine Rule
A
c b
B a x C

2. Cosine Rule
A
c b
h
B a x C

3. Cosine Rule
A
h2  b2  x2
c b
h
B a x C

4. Cosine Rule
A
h2  b2  x2
c2  h2   a  x 
2
c b
h
B a x C

5. Cosine Rule
A
h2  b2  x2
c2  h2   a  x 
2
c b
h  c 2  b 2  x 2  a 2  2ax  x 2
 b 2  a 2  2ax
B a x C

6. Cosine Rule
A
h2  b2  x2
c2  h2   a  x 
2
c b
h  c 2  b 2  x 2  a 2  2ax  x 2
 b 2  a 2  2ax
B a x C x
But  cos C
b
x  b cos C

7. Cosine Rule
A
h2  b2  x2
c2  h2   a  x 
2
c b
h  c 2  b 2  x 2  a 2  2ax  x 2
 b 2  a 2  2ax
B a x C x
But  cos C
b
x  b cos C
 c 2  b 2  a 2  2ab cos C

8. Cosine Rule
A
h2  b2  x2
c2  h2   a  x 
2
c b
h  c 2  b 2  x 2  a 2  2ax  x 2
 b 2  a 2  2ax
B a x C x
But  cos C
b
In any ABC x  b cos C
a  b  c  2bc cos A
2 2 2  c 2  b 2  a 2  2ab cos C
b 2  a 2  c 2  2ac cos B
c 2  a 2  b 2  2ab cos C

9. e.g.  i 
7 T
F 98 13

3
t
M

10. e.g.  i 
7 t 2  f 2  m 2  2 fm cos T
T
F 98 13

t 2  32  7 2  2  3 7  cos9813
3
t
M

11. e.g.  i 
7 t 2  f 2  m 2  2 fm cos T
T
F 98 13

t 2  32  7 2  2  3 7  cos9813
3 t  8 units (to nearest whole number)
t
M

12. e.g.  i 
7 t 2  f 2  m 2  2 fm cos T
T
F 98 13

t 2  32  7 2  2  3 7  cos9813
3 t  8 units (to nearest whole number)
t
A M
(ii )
15
F 20
6
S

13. e.g.  i 
7 t 2  f 2  m 2  2 fm cos T
T
F 98 13

t 2  32  7 2  2  3 7  cos9813
3 t  8 units (to nearest whole number)
t
A M
(ii ) f 2  a 2  s 2  2as cos F
15
a2  s2  f 2
cos F 
2as
F 20
6
S

14. e.g.  i 
7 t 2  f 2  m 2  2 fm cos T
T
F 98 13

t 2  32  7 2  2  3 7  cos9813
3 t  8 units (to nearest whole number)
t
A M
(ii ) f 2  a 2  s 2  2as cos F
15
a2  s2  f 2
cos F 
2as
F 20
62  152  202
cos F 
6 2  6 15 
S

15. e.g.  i 
7 t 2  f 2  m 2  2 fm cos T
T
F 98 13

t 2  32  7 2  2  3 7  cos9813
3 t  8 units (to nearest whole number)
t
A M
(ii ) f 2  a 2  s 2  2as cos F
15
a2  s2  f 2
cos F 
2as
F 20
62  152  202
cos F 
6 2  6 15 
F  14033
S

16.  iii  A

7
25
B
b
3
C

17.  iii  A

7
25
B
b
3
C
a 2  b 2  c 2  2bc cos A
32  b 2  7 2  2b  7  cos 25
9  b 2  49  14b cos 25

18.  iii  A

7
25
B
b
3
C
a 2  b 2  c 2  2bc cos A
32  b 2  7 2  2b  7  cos 25
9  b 2  49  14b cos 25
b 2  14b cos 25  40  0

19.  iii  A

7
25
B
b
3
C
a 2  b 2  c 2  2bc cos A
32  b 2  7 2  2b  7  cos 25
9  b 2  49  14b cos 25
b 2  14b cos 25  40  0
14cos 25  196cos 2 25  160
b
2

20.  iii  A

7
25
B
b
3
C
a 2  b 2  c 2  2bc cos A
32  b 2  7 2  2b  7  cos 25
9  b 2  49  14b cos 25
b 2  14b cos 25  40  0
14cos 25  196cos 2 25  160
b
2
b  5.85 units or b  6.85 units (to 2 dp)

21. Exercise 4I; 1a, 2b, 4, 5, 7, 9, 11, 12, 13, 14*
Exercise 4J; evens