What is the ambiguous case for the law of sines?

Law of Sines–Ambiguous Case For those of you who need a reminder, the ambiguous case occurs when one uses the law of sines to determine missing measures of a triangle when given two sides and an angle opposite one of those angles (SSA).

How many possible answers are there in the ambiguous case of the law of sines?

There are six different scenarios related to the ambiguous case of the Law of sines: three result in one triangle, one results in two triangles and two result in no triangle. We’ll look at three examples: one for one triangle, one for two triangles and one for no triangles.

How do you know if the law of sines has two solutions?

If their sum is less than 180°, you have two valid answers. If the sum is over 180°, then the second angle is not valid.

How do you know if a triangle is ambiguous?

If the side opposite the given angle is equal in length to the other given side, then A = B, and one isosceles triangle is determined. If the side opposite the given angle is longer than the other given side, then < 1, and one triangle is determined.

Is there an ambiguous case for the cosine law?

Unlike the Ambiguous Case for the Law of Sines with all of its possible situations, the Ambiguous Case for the Law of Cosines leaves the decision making on the number of triangles (or solutions) to the quadratic equation. (2) if the solution is “two Real positive values”, there are two possible triangles (2 solutions).

What is the ambiguous case and why could it have two solutions?

The “Ambiguous Case” (SSA) occurs when we are given two sides and the angle opposite one of these given sides. The triangles resulting from this condition needs to be explored much more closely than the SSS, ASA, and AAS cases, for SSA may result in one triangle, two triangles, or even no triangle at all!

Why does the ambiguous case occur?

Why does the ambiguous case not occur in cosine law?

Originally Answered: Why are there only ambiguous cases in triangles for sine law and not cosine law? Because all angles of a triangle are between 0 and 180 degrees, there is only one angle with a given cosine and two angles with a given sine.

When can you use the law of sines to find a missing angle?

This law is useful for finding a missing angle when given an angle and two sides, or for finding a missing side when given two angles and one side.

What is the ambiguous case of sines?

For those of you who need a reminder, the ambiguous case occurs when one uses the law of sines to determine missing measures of a triangle when given two sides and an angle opposite one of those angles (SSA)…. If angle A is acute, and a = h, one possible triangle exists If angle A is acute, and a < h, no such triangle exists.

What is the ambiguous case in math?

Explanation: For those of you who need a reminder, the ambiguous case occurs when one uses the law of sines to determine missing measures of a triangle when given two sides and an angle opposite one of those angles (SSA). If angle A is acute, and a < h, no such triangle exists.

What is the ambiguous case of SSA?

Explanation: For those of you who need a reminder, the ambiguous case occurs when one uses the law of sines to determine missing measures of a triangle when given two sides and an angle opposite one of those angles (SSA)…. If angle A is acute, and a = h, one possible triangle exists If angle A is acute, and a < h, no such triangle exists.

What is the sine of an obtuse angle ABC?

The trigonometric functions (sine, cosine, etc.) are defined in a right triangle in terms of an acute angle. What, then, shall we mean by the sine of an obtuse angle ABC? The sine of an obtuse angle is defined to be the sine of its supplement.