The Law of Sines 16'1

1
The Law of Sines (16.1)
2

• Solving Oblique Triangles

B
Drop altitude to side AC
12
x
68?
55?
A
C
? x sin 68? 12 sin 55?
Sin 55? h
Sin 68? h
x
12
x 12 sin 55?
? 10.6
sin 68?
x sin 68? h
12 sin 55? h
3
Analyze x sin 68? 12 sin 55?
Can be written as a proportion
sin 68? sin 55?
12
x
The Law of Sines
If a, b, and c are the lengths of the sides
opposite angles A, B, and C respectively in
triangle ABC, then
sinA sinB sinC
a
b
c
OR
sinA sinB sinC
a
b
c
4
Sketchpad Example
5
Example
Find p and q
P
q
40?
14
110?
30?
R
Q
p
Use angle and opposite side that are known or can
be found
sin 30
sin 110
p 18.0
14
q
q sin 30 14 sin 110
q 14 sin 110
? 26.3
Sin 30