Law of Sines

1
Law of Sines

• Lesson 6.4

2
The Law of Sines

• Lets now solve oblique triangles (?s without a
  right angle)

3
When to Use the Law of Sines

• When we know one side and two angles (ASA or SAA)
• When we know two sides and an angle opposite one
  of those sides (SSA)
• Basically, we need to know a side and the angle
  opposite that side

C 112
a
b 216.75
B
44.5
c
A 23.5
4
Using the Sine Law

• We know 2 sides and angle opposite one of the
  sides
• Now how would we find angle C and then side c?

C
a 9.5
b15
A
c
B 47
5
Example 1 A satellite orbiting the earth passes
directly overhead and between Phoenix and L.A.,
340 mi apart. The angle of elevation is
simultaneously observed to be 60 at Phoenix and
75 at L.A. How far is the satellite from L.A.?

60
75
340 mi
6
Ex 1 Solution How far is the satellite from L.A.?
sat
45
c
b
60
75
340 mi
LA
PHO
7
Height of a Kite

• Two observers directly under the string and 30'
  from each other observe a kite at an angle of 62
  and 78. How high is the kite?

h
78
62
30
8
Height of a Kite (contd)
h
78
62
30
9
The Ambiguous Case (SSA)

• Given two sides and an angle opposite one of
  them, several possibilities exist
• No solution,side too shortto make a triangle
• One solution,side equalsaltitude

2
10
20
10
The Ambiguous Case (SSA)

• Two solutions 2 triangles are possible (why?)
• One unique solution,the opposite sideis longer
  thanadjacent side

Solving for A could give either an acute or
obtuse angle!
10
5 5
20
A
A'
13.42
10
20