1. Warm-up
Determine the measure of the missing angle, theta in the obtuse triangle below.
2.7
3.0
46o

2. Homework Issues???
(page 163 # 2, 3; page 170 # 5, 7, 10, )

3. The
of the Sine Law

4. By definition, the word ambiguous means open to two or more interpretations.
Such is the case for certain solutions when working with the 
Law of Sines.
If you are given two angles and a side opposite (ASA or AAS), the Law of Sines will nicely provide you with ONE solution for a missing side.

Unfortunately, the Law of Sines has a problem dealing with SSA. If you are given information about two sides and one angle which is not contained, with no diagram, there could be zero, one, or two possible triangles that could be drawn.

5. For Example:
In triangle ABC, angle A = 30 degrees, b = 5 and a = 3. Determine the length of c.

6. How can we determine how many possible triangles there are based on a particular situation???
We can always start be determining the height of the triangle.

7. height of triangle C A B B'

8. a < b sinA, there is no solution a = b sinA, there is ONE solution
So, if:
a < b sinA, there is no solution
a = b sinA, there is ONE solution
a > b sinA, there are TWO solutions
a > b, there is ONE triangle only.
height of triangle
Note: a is the side opposite the angle. C A B b a
a<bsinA = no triangle
a=bsinA = one rt < triangle
a>bsinA = two possible triangles

9. http://jwilson. coe. uga. edu/EMT668/EMAT6680

10. In triangle ABC, angle A = 47 degrees, b = 10 cm
In triangle ABC, angle A = 47 degrees, b = 10 cm. Find possible values of side "a" that would result in ....
a) no triangles
b) 1 right triangle
c) 2 triangles
d) 1 obtuse triangle.

14. Textbook Questions:
Pages
# 4, 5, 6, 7, 9, 11
*Due tomorrow!

16. In triangle ABC angle A = 50 degrees, side b = 14 cm and
side a = 12 cm. Calculate the measures of angles B and C.

17. Example 1: In triangle ABC, <A = 42o, a = 7. 2cm and b = 8. 5cm
Example 1: In triangle ABC, <A = 42o, a = 7.2cm and b = 8.5cm. Find <B and <C.

18. C
15m
12m
120o B A