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 * **How can the Law of Sines be used in problems involving the "ambiguous case"?**

At the end of this lesson, you will be able to...
 * 1) apply the Law of Sines to discover all the values of an unknown angle
 * 2) determine when a problem might lead to an ambiguous case

In this lesson, you will discover that not all examples that use the Law of Sines to solve will work out nicely. Some problems will lead to triangles that might have two different answers, hence the ambiguous case. You will learn how to anticipate which triangles will give this case.

We learned in the last lesson/page that the problems work out nicely when we know AAS for a triangle or ASA for a triangle.

Copy these questions into your notebook. Answer them as you watch the videos.


 * 1) Which type of triangle will give us the ambiguous case?
 * 2) What happens when sin x >1?
 * 3) What happens when the sin x <1?
 * 4) How do we determine if there are one or two answers?

This video gives a lot of front loaded information. It seems a lot but the instructor gives some rules to help you.

[|Video 1]

[|Video 2]


 * **Classwork:** Now try some on your own. Be sure to draw a picture before doing any work. Remember: if a triangle is given information that is SSA, that is the ambiguous case. You need to check to see if 0, 1, 0r 2 triangles exist.


 * 1) In triangle ABC, a=8, b=16, and angle A = 30. Find angle B.
 * 2) In triangle DEF, d=16, e=8, and angle D = 30. Find angle E.
 * 3) In triangle GHI, g = 8, h = 20, and angle G = 30. Find angle H.


 * **Homework:** Complete #3-17 odd. Watch out for the SSA triangles!!!

[|Ambiguous_Case.JPG]


 * **Answers**

[|A-Ambiguous_Case.JPG]


 * **Journal entry:** When a Kodiak bear fishes for his breakfast in the river, the bear is aware that the fish is not located in the position in which he sees it. People understand that this is because a beam of light that strikes the surface of the river water is bent or refracted. This relationship between the speed of light, both in and out of the water, is described as Snell's Law. How is Snell's law related to the Law of Sines?