1. The Sine Rule. A B C ao bo co

2. Finding The Sine Rule. Consider the triangle below: C A B ao bo co H
Add the altitude line as shown.
H is the height of the triangle.
Now write the sine ratio for each right angled triangle:
H =
A sin bo
H =
B sin ao
Look at these two results and try to work out the next line:

3. C A B ao bo co
H =
A sin bo
B sin ao
A sin bo = B sin ao
Now divide both sides by sin bo and sin ao .
By changing the letters around we can prove that:
The Sine Rule.

4. Calculating Sides Using The Sine Rule.
Example 1
Find the length of L in this triangle.
10m
34o
41o L
Match up corresponding sides and angles:
Now cross multiply.
Solve for L.

5. Example 2
Find the length of L in this triangle.
10m
133o
37o L
Match up corresponding sides and angles:
Now cross multiply.
Solve for L.
= 12.14m

6. What Goes in the Box ? 1
Find the unknown side in each of the triangles below:
(1)
12cm
72o
32o A
B = 21.8mm
(2)
93o B
47o
16mm
A = 6.7cm
(4)
143o D
12o
17m
(3)
87o
89m
35o C
C = 51.12m
D = 49.21m

7. Calculating Angles Using The Sine Rule.
Example 1. ao
45m
23o
38m
Find the angle ao
Match up corresponding sides and angles:
Now cross multiply:
Solve for sin ao
= 0.463
Use sin to find ao

8. Example 2.
143o
75m
38m bo
Find the size of the angle bo
Match up corresponding sides and angles:
Cross multiply.
Solve for sinbo
= 0.305
Use sin to find bo

9. What Goes In The Box ? 2 Calculate the unknown angle in the following:
(2)
14.7cm bo
14o
12.9cm
(1)
14.5m
8.9m ao
100o
ao = 37.2o
(3)
93o
64mm co
49mm
bo = 16o
c =49.9o