sine rule
TRANSCRIPT
C
B
A
13 Apr 2023
Sine Rule
a
b
c
The Sine Rule can be used with ANY triangle as long as we have been given enough information.
Works for any Triangle
a b c= =
SinA SinB SinC
Deriving the rule
B
C
A
b
c
a
Consider a general triangle ABC.
The Sine Rule
Draw CP perpendicular to BA
P
CPSinB CP aSinB
a
CP
also SinA CP bSinAb
aSinB bSinA
aSinBb
SinA
a bSinA SinB
This can be extended to
a b cSinA SinB SinC
or equivalentlySinA SinB SinCa b c
Calculating Sides Using The Sine Rule
10m
30o
45o
a
Match up corresponding sides and angles:
Now cross multiply.
Solve for a.
Example 1 : Find the length of a in this triangle.
A
B
C
𝑎sin 45°
=¿
𝑎 sin 30°=10sin 45°
𝑎=10sin 45°
sin 30°
10
sin 30°
𝑎=10.12
√2
12
=10√2
13 Apr 2023
What goes in the Box ?
Find the unknown side in each of the triangles below:
(1) 12cm
60o
30o
a
(2)
60o
b45o
16mm
a = cmb = mm
13 Apr 2023
Now try Ex 6&7 Ch8 (page 103)
Sine Rule
13 Apr 2023
Starter Questions
1. Factorise 9x - 36
2. Find the gradient and the y - intercept
3 1 f or the line with equation y = - x +
4 5
3. Write down the two values of cos
1 that give you a value of
2
13 Apr 2023
Learning Intention Success Criteria
1. Know how to use the sine rule to solve problems involving angles.
1. To show how to use the sine rule to solve problems involving finding an angle of a triangle .
Sine Rule
Calculating Angles Using The Sine Rule
Example 1 :
Find the angle Ao
Ao
45m
23o
38m
Match up corresponding sides and angles:
45
sin oA 38
sin 23oNow cross multiply:
38sin 45sin 23o oA Solve for sin Ao
45sin 23sin
38
ooA = 0.463 Use sin-1 0.463 to find Ao
1sin 0.463 27.6o oA
Calculating Angles
Using The Sine Rule
143o
75m
38m
Bo
38
sin oB
75sin 38sin143o oB
75
sin143o
38sin143sin
75
ooB = 0.305
1sin 0.305 17.8o oB
Example 2 :
Find the angle Bo
Match up corresponding sides and angles:
Now cross multiply:
Solve for sin Bo
Use sin-1 0.305 to find Bo
What Goes In The Box ?
Calculate the unknown angle in the following:
(1)
14.5m
8.9m
Ao
100o (2)
14.7cm
Bo
14o
12.9cm
Ao = 37.2o
Bo = 16o