What is an ambiguous case in trigonometry?

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!

How do you know if a triangle is ambiguous?

1 Answer

1. If angle A is acute, and a < h, no such triangle exists.
2. If angle A is acute, and a = h, one possible triangle exists.
3. If angle A is acute, and a > b, one possible triangle exists.
4. If angle A is acute, and h < a < b, two possible triangles exist.

What is ambiguous case in sine rule?

Ambiguous Case



A common application of the sine rule is to determine the triangle A B C ABC ABC given some of its sides and angles. The ambiguous case refers to scenarios where there are 2 distinct triangles that satisfy such a configuration.

How do you find the ambiguous case angle?

The Ambiguous Case of the Law of Sines

1. See if you are given two sides and the angle not in between (SSA). …
2. Find the value of the unknown angle.
3. Once you find the value of your angle, subtract it from 180° to find the possible second angle.
4. Add the new angle to the original angle.

How do you determine if you have 0 1 or 2 triangles for the ambiguous case?

Video quote: All you need to do is determine is at one shot one two or three triangles.

Which case of oblique triangles is also known as the ambiguous case?

An interesting problem arises when two sides and an angle opposite one of them are known. This is called the ambiguous case. A unique triangle is not always determined. The possible solutions depend on whether the given angle is acute or obtuse.

How do you find the height of an ambiguous case?

The height is the perpendicular distance from the upper vertex to the base. Because there is a right angle between the height and base, we can always use the fixed angle and the length of the fixed side to determine the height.

How do you solve ambiguous problems?

5 Tips to Overcome Ambiguity at Work

1. Learn to Act without Knowing All of the Details. Having the ability to take action without having each and every detail is a key component in dealing with ambiguity. …
2. Confidently Take Risks. …
3. Plan for Different Scenarios. …
4. Communicate. …
5. Embrace Change.

Feb 8, 2022

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.

What are the possible outcomes of the ambiguous case?

In this ambiguous case, three possible situations can occur: 1) no triangle with the given information exists, 2) one such triangle exists, or 3) two distinct triangles may be formed that satisfy the given conditions.

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.

What is SAS triangle?

first such theorem is the side-angle-side (SAS) theorem: If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.

How do we know if a triangle exist or not?

All you have to do is use the Triangle Inequality Theorem, which states that the sum of two side lengths of a triangle is always greater than the third side. If this is true for all three combinations of added side lengths, then you will have a triangle.

How do you know if 3 sides make a right triangle?

Video quote: And then again a and B are the lengths of the legs. So let's let a equal 12 and B equal 35.

Can a triangle be formed with side lengths 10 12 22?

No; 10. SOLUTION: The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

What kind of triangle has angles 60 60 and 60?

Isosceles Triangle

Isosceles Triangle degrees 60, 60, 60 | ClipArt ETC.

Do triangles have 4 sides?

The triangle has three (3) sides. The triangle is a polygon that contains three sides and three inner angles and three vertices.

What do you call a triangle with no equal sides?

Scalene. A scalene triangle has three different angles and none of its sides are equal in length.

What angle type is in a pentagon?

Types of Pentagon

What degrees is a hexagon?

A hexagon has six sides, and we can use the formula degrees = (# of sides – 2) * 180. Then degrees = (6 – 2) * 180 = 720 degrees. Each angle is 720/6 = 120 degrees.

What is a Nonagon shape?

A nine-sided shape is a polygon called a nonagon. It has nine straight sides that meet at nine corners, or vertices. The word “nonagon” comes from the Latin word “nona”, meaning nine, and “gon”, meaning sides. So it literally means “nine sided shape”.

How many sides does a Dodecagon have?

A dodecagon is a 12-sided polygon. Several special types of dodecagons are illustrated above. In particular, a dodecagon with vertices equally spaced around a circle and with all sides the same length is a regular polygon known as a regular dodecagon.

How many sides has pentagon?

The word Pentagon is derived from a Greek word, pente, meaning five sides or a five-sided polygon. So, whatever the object is, if it possesses five sides or five angles or corners, it can be termed as a pentagon.



List of other polygons.

Is a hexagon an equilateral?

A hexagon is made up of 6 congruent equilateral triangles. Each equilateral triangle has a length of 8 units.