8-2 Law of Sines

1
8-2 Law of Sines

• What if the triangle information is given in
  profane form
• (oops!!)

2
Try this

• Solve ?ABC if a 50, c 65 and A 57º
• What happened?

a
c
Fixed
A
b
3
What happened?

• The data was such that the triangle is just
  impossible. Are there other possibilities?
• Yes there are 4

4
a
c
c
a
A
A
b
b
a too short
a just perfect
c
a
c
a
A
b
A
b
a just a little bigger
a too big to hit twice
5
a
c
c
a
A
A
b
b
a lt csinA
a csinA
c
a
c
a
A
b
A
b
csinA lt a lt c
a c
6
How do we deal with this?

• Remember The calculator only gives the Q1
  answer (function theory). SO, you have to figure
  out what the Q2 answer would be and see if the
  triangle can still exist.
• Q1 Q2 180

7
What is the process to follow?

• If ASS triangle (given 1 angle)
• Determine second angle.
• Determine what third angle would be with given
  and second angles.
• Determine second angles supplement.
• Determine what third angle would be with given
  angle and second angles supplement.
• Determine the last side based both on the last
  angle (step 2) and other option (step 4)

8
Examples

• The first example we did, where you get error
  or E as a solution that means that there is
  no triangle possible.
• Solve for ?ABC if c 65, a 60 and
• A 57º
• 3. Solve for ?ABC if c 65, a 68 and
• A 57º