Ambiguous Case Of Law Of Sines Math

Three result in one triangle one results in two triangles and two result in no triangle. Ambiguous means open to two or more interpretations. When dealing with the law of sines you will be looking to find an angle.

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That is the reason we call this case ambiguous.

Ambiguous case of law of sines math. We can shorten this situation with ssa. S i n e e s i n f f s i n e 27 s i n 37 12 s i n e 27 s i n 37 12 s i n b 1 3541 no solution. The law of sines. As you can see two different angles have the same sine value.

For example take a look at this picture. There are six different scenarios related to the ambiguous case of the law of sines. S i n b 1 3541. Since the length of the third side is not known we don t know if a triangle will be formed or not.

The ambiguous case of the law of sines happens when two sides and an angle opposite one of them is given. The law of sines relates all angles and sides of a triangle in the following way in which the lowercase letters indicate the side directly across from the capitalized angle. And it is the foundation for the ambiguous case of the law of sines. If you are told that b 10 in.

The maximum value of the sine function is 1. What angle measurement has a sine value of frac 1 2. For problems in which we use the law of sines given one angle and two sides there may be one possible triangle two possible triangles or no possible triangles. This is what we mean by ambiguous.

Find all possible m e to the nearest degree. Before we dive into the ambiguous case let s review the law of sines and congruence. This is a big deal. So if i asked you.

Ambiguous case of the law of sines. If two sides and the non included angle are given three situations may occur. 1 no triangle exists no solution. And c 6 in there are two different triangles that match this criteria.

You could say two different things either 30 circ or 150 circ. For this reason ssa is referred to as the ambiguous case. This situation is also known as the ambiguous case. As you can see in the picture either an acute triangle or an obtuse triangle could be created because side c could swing either in or out along the unknown side a.

Remember ambiguous means that something has more than 1 meaning. When using the law of sines to find an unknown angle you must watch out for the ambiguous case. There is no possible e with the given dimensions. This occurs when two different triangles could be created using the given information.