Ambiguous Law Of Sines Math

B sin b a sin a b a sinb sina 10 sin64 sin 41 b 13 7 and c sin c a sin a c a sinc sin a 10 sin75 sin 41 c 14 7.

Ambiguous law of sines math. There are six different scenarios related to the ambiguous case of the law of sines. This occurs when two different triangles could be created using the given information. This situation is also known as the ambiguous case. This is a big deal.

A sin a 7 sin 35 c sin 105 ignore a sin a not useful to us. For example take a look at this picture. Ambiguous case of the law of sines. The sine of an obtuse angle.

As you can see two different angles have the same sine value. A sin a b sin b c sin c put in the values we know. It does not come up in calculus. The law of sines.

There is no possible e with the given dimensions. The ambiguous case of the law of sines happens when two sides and an angle opposite one of them is given. B 180 a c 180 41 75 b 64. Right acute or obtuse triangles.

And c 6 in there are two different triangles that match this criteria. 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. And it is the foundation for the ambiguous case of the law of sines. So by the law of sines we have.

Proof of the law of sines this is a topic in traditional trigonometry. S i n b 1 3541. 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. It is valid for all types of triangles.

We can shorten this situation with ssa. It states the following. 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.

Since the length of the third side is not known we don t know if a triangle will be formed or not. The law of sines can be used to compute the remaining sides of a triangle when two angles and a side are known aas or asa or when we are given two sides and a non enclosed angle ssa. Before we dive into the ambiguous case let s review the law of sines and congruence. The law of sines.

The law of sines is also known as the sine rule sine law or sine formula. Case 2 two sides and one opposite angle known. T he law of sines allows us to solve triangles that are not right angled and are called oblique triangles. What angle measurement has a sine value of frac 1 2.

Three result in one triangle one results in two triangles and two result in no triangle. If you are told that b 10 in. Statement of the law of sines. 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.

That is the reason we call this case ambiguous.