11x1 t04 05 sine rule (2011)
TRANSCRIPT
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*