11 x1 t04 06 cosine rule (2013)
TRANSCRIPT
Cosine RuleA
B Ca
bc
x
Cosine RuleA
B C
h
a
bc
x
Cosine RuleA
B C
h
a
bc
2 2 2h b x
x
Cosine RuleA
B C
h
a
bc
2 2 2h b x
x
22 2c h a x
Cosine RuleA
B C
h
a
bc
2 2 2h b x
2 2 2 2 22c b x a ax x
x
22 2c h a x
2 2 2b a ax
Cosine RuleA
B C
h
a
bc
2 2 2h b x
2 2 2 2 22c b x a ax x
x
22 2c h a x
2 2 2b a ax
But cos
cos
x Cbx b C
Cosine RuleA
B C
h
a
bc
2 2 2h b x
2 2 2 2 22c b x a ax x
x
22 2c h a x
2 2 2b a ax
But cos
cos
x Cbx b C
2 2 2 2 cosc b a ab C
Cosine RuleA
B C
h
a
bc
2 2 2h b x
2 2 2 2 22c b x a ax x
2 2 2
In any ABC2 cosa b c bc A
x
22 2c h a x
2 2 2b a ax
But cos
cos
x Cbx b C
2 2 2 2 cosc b a ab C
2 2 2 2 cosb a c ac B 2 2 2 2 cosc a b ab C
e.g. iTF
M
t
98 13
3
7
e.g. iTF
M
t
98 13
3
2 2 2 2 cost f m fm T 7 2 2 23 7 2 3 7 cos98 13t
e.g. iTF
M
t
98 13
3
2 2 2 2 cost f m fm T
8 units (to nearest whole number)t
7 2 2 23 7 2 3 7 cos98 13t
e.g. iTF
M
t
98 13
3
2 2 2 2 cost f m fm T
8 units (to nearest whole number)t
( )ii
F
A
S
20
6
7 2 2 23 7 2 3 7 cos98 13t
15
e.g. iTF
M
t
98 13
3
2 2 2 2 cost f m fm T
8 units (to nearest whole number)t
( )ii
F
A
S
20
6
2 2 2 2 cosf a s as F 2 2 2
cos2
a s fFas
7 2 2 23 7 2 3 7 cos98 13t
15
e.g. iTF
M
t
98 13
3
2 2 2 2 cost f m fm T
8 units (to nearest whole number)t
( )ii
F
A
S
20
6
2 2 2 2 cosf a s as F 2 2 2
cos2
a s fFas
7 2 2 23 7 2 3 7 cos98 13t
15
2 2 26 15 20cos2 6 15
F
e.g. iTF
M
t
98 13
3
2 2 2 2 cost f m fm T
8 units (to nearest whole number)t
( )ii
F
A
S
20
6
2 2 2 2 cosf a s as F 2 2 2
cos2
a s fFas
140 33F
7 2 2 23 7 2 3 7 cos98 13t
15
2 2 26 15 20cos2 6 15
F
iii
B
A
b
257
C3
iii
B
A
b
257
C3
2 2 2 2 cosa b c bc A
2 2 2
2
3 7 2 7 cos 25
9 49 14 cos 25
b b
b b
iii
B
A
b
257
C3
2 2 2 2 cosa b c bc A
2 2 2
2
3 7 2 7 cos 25
9 49 14 cos 25
b b
b b
2 14 cos 25 40 0b b
iii
B
A
b
257
C3
2 2 2 2 cosa b c bc A
2 2 2
2
3 7 2 7 cos 25
9 49 14 cos 25
b b
b b
2 14 cos 25 40 0b b
214cos 25 196cos 25 1602
b
iii
B
A
b
257
C3
2 2 2 2 cosa b c bc A
2 2 2
2
3 7 2 7 cos 25
9 49 14 cos 25
b b
b b
2 14 cos 25 40 0b b
214cos 25 196cos 25 1602
b
5.85 units or 6.85 units (to 2 dp)b b
Exercise 4I; 1a, 2b, 4, 5, 7, 9, 11, 12, 13, 14*
Exercise 4J; evens