The Ambiguous Case 7'2

1
The Ambiguous Case7.2

• JMerrill, 2007

2
Ambiguous Case
When two sides and a non-included angle are
given, there are several situations possible
this is the ambiguous case.
There could be only one triangle. There could be
two triangles (when you can fit the alternate
angle in a triangle). There could be no triangle
(when you take the inverse sine of a value larger
than 1).
3
Example

• Find angle B in triangle ABC if a 2, b 6, and
  A 30o
• Applying the Law of Sines, we have

Since sinB can never be larger than 1, this
triangle does not exist.
4
Example 2

• Find the missing parts in triangle ABC if a
  54cm, b 62cm, and A 40o
• First solve for B
• Since B can be 48o or 132o, C can be 92o or 8o
• Then c can be 84cm or 12cm (using Law of Sines)

Thus, there are 2 possibilities and no way to
tell which is correctambiguous!
5
Example 3-Application
A forest ranger at an observation point (A)
sights a fire in the direction 32 east of north.
Another ranger at a second observation point
(B), 10 miles due east of A, sights the same fire
48 west of north. Find the distance from each
observation point to the fire.
80o
48o
32o
42o
58o
10
B
A