the sine rule
DESCRIPTION
The Sine Rule. C. McMinn. a sin A. b sin B. c sin C. ==. SOH/CAH/TOA can only be used for right-angled triangles. The Sine Rule can be used for any triangle:. C. b. The sides are labelled to match their opposite angles. a. A. B. c. The Sine Rule:. A. Example 1 :. - PowerPoint PPT PresentationTRANSCRIPT
The Sine Rule
C. McMinn
SOH/CAH/TOA can only be used for right-angled triangles.
The Sine Rule can be used for any triangle:
A B
C
ab
c
The sides are labelled to match their opposite angles
asinA
bsinB
csinC
= =The Sine Rule:
Example 1:
C B
A
76º
7cm
Find the length of BC
x
a
sinA
c
sinC
bc
a
=
x
sin76º
7
sin63º= × sin76ºsin76º ×
x =7
sin63º× sin76º
x = 7.6 cm
63º
Draw arrows from the sides to the opposite angles to help decide which parts of the sine rule to use.
Draw arrows from the sides to the opposite angles to help decide which parts of the sine rule to use.
Example 2:
Q R
P
55º
82º
15cm
Find the length of PR
x
p
sinP
q
sinQ
r q
p
=
15
sin82º
x
sin43º= × sin43ºsin43º ×
= x15
sin82ºsin43º ×
x = 10.33 cm
43º
Draw arrows from the sides to the opposite angles to help decide which parts of the sine rule to use.
Draw arrows from the sides to the opposite angles to help decide which parts of the sine rule to use.
1. 2. 3.
4. 5.6.
7.
A
B
C
D E
F
G
H I
P
Q
R
62º
53º
5 cm
x28º 130º
13 cmx
41º
76º
x
26 mm
37º
77º10 m
x 5.2 cm
57º
x62º
x86º
35º
12 cm
x
85º
65º
6 km
5.5 8.0
10.7
66º
35.3
63º
61º
5.2
6.9
6.6
Remember:
• Draw a diagram• Label the sides• Set out your working exactly as you have been
shown• Check your answers regularly and ask for help if you
need it
Finding an Angle
The Sine Rule can also be used to find an angle, but it is easier to use if the rule is written upside-down!
sinA a
sinBb
sinC c
= =Alternative form of the Sine Rule:
Example 1:
A B
C
72º
6cm
Find the size of angle ABC
x º
sinA
a
sinB
b
ba
c
=
sin72º
6
sin xº
4= × 44 ×
= sin xº4 ×
sin xº = 0.634
Draw arrows from the sides to the opposite angles to help decide which parts of the sine rule to use.
Draw arrows from the sides to the opposite angles to help decide which parts of the sine rule to use.
4cm
sin72º
6
x = sin-1 0.634 = 39.3º
Example 2:
R Q
P
85º
8.2cm
Find the size of angle PRQ
x º
sinP
p
sinR
r
qr
p
=
sin85º
8.2
sin xº
7= × 77 ×
= sin xº7 ×
sin xº = 0.850
7cm
sin85º
8.2
x = sin-1 0.850 = 58.3º
1.2. 3.
4.5.
6. 7.
47º
6 cmxº
5 cm
xº
105º
8.8 cm
6.5cm
xº
33º 5.2 cm
5.5 cm
xº
7.6 cm
8.2
cm
xº
82º
8 m
70º
9.5
m
(←Be careful!→)
xº
27º
6 km
3.5 km
74º
xº
7 mm
9 mm
37.6°66.6°
45.5°
31.0°
51.1°
57.7°
92.1°52.3º 22.9º
Remember:
• Draw a diagram• Label the sides• Set out your working exactly as you have been
shown• Check your answers regularly and ask for help if you
need it