1. Trigonometry (1)
Sine Rule
Cosine Rule

2. [Height] h2 = b2 - x2
[Height] h2 = a2 - (c-x)2
h2 = a2 - c2 +2cx - x2 C
b2 - x2 = a2 - c2 +2cx - x2
+x2
+x2 a
b2 = a2 - c2 +2cx b h
b2 = a2 - c2 +2c x b cos A
a2 = b2 + c2 - 2bc cos A B A x
c-x c
cos A = Adj/Hyp = x/b
x = b cos A
The cosine rule proof - won’t be examined

3. The Cosine Rule a2 = b2 + c2 - 2bc cos A b2 = a2 + c2 - 2ac cos B
… is used for working out angles and sides in non-right angled triangles
a2 = b2 + c2 - 2bc cos A
It is …. C
angles a
sides b A B c
By similar proofs:-
b2 = a2 + c2 - 2ac cos B
c2 = a2 + b2 - 2ab cos C

4. The Cosine Rule - example
Finding a side
a2 = b2 + c2 - 2bc cos A C
angles
sides 6
a ?
75o A B 8
a2 = x6x8 cos 75
a2 = x
a2 =
a =8.67 cm [2 d.p.]

5. The Cosine Rule - example
Finding an angle
a2 = b2 + c2 - 2bc cos A C
angles
sides
7.1
13.5 ? A B
8.8
13.52 = x7.1x8.8 cos A
2x7.1x8.8 cos A =
cos A = =
2x7.1x8.8
A = 116o [to nearest degree]

6. Turn to page 71 of your Core 2 book and answer …
Activity
Turn to page 71 of your Core 2 book and answer …
exercise B
1a)
2a)

7. sin A = Opp/Hyp = h/b C
h = b sin A
sin B = Opp/Hyp = h/a
h = a sin B a
If the perpendicular was here b h
h = b sin A = a sin B B
sin A sin B
a = b A c
The sine rule proof - won’t be examined
sin B sin C
b = c

8. The Sine Rule It is …. a = b = c sin A sin B sin C C angles a sides b
… is used for working out angles and sides in non-right angled triangles
It is …. a = b = c
sin A sin B sin C C
angles a
sides b A B c

9. The Sine Rule - example a = b = c sin A sin B sin C a = b a = 4
Finding a side
a = b = c
sin A sin B sin C C
angles
sides
4 cm
a ?
75o
35o A B
a = b
sin A sin B
a = 4
sin sin 75
a = x sin 35 = = 2.4 cm [1dp]
sin 75

10. The Sine Rule - example a = b = c sin A sin B sin C a = b 4 = 6.5
Finding an angle
a = b = c
sin A sin B sin C C
angles
sides
6.5 cm
4 cm
85o ? A B
a = b
sin A sin B =
sin A sin 85
4 x sin 85 = x sin A
sin A = 4 x sin 85 =
6.5
A = 38o or
= 162o

11. Turn to page 74 of your Core 2 book and answer …
Activity
Turn to page 74 of your Core 2 book and answer …
exercise C
1a)
3a)