How do you determine if a triangle is ambiguous?
How do you determine if a triangle is ambiguous?
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!
What are the possible outcomes of the ambiguous case?
In the ambiguous case, there are three possible outcomes: No triangle exists that has the given measures; there is no solution. One triangle exists that has the given measures; there is one solution.
How do you know how many triangles possible?
Since there is exactly one triangle, there is one solution. Case 3 is referred to as the Ambiguous Case because there are two possible triangles and two possible solutions….SSA Triangles.
| If: | Then: | |
|---|---|---|
| c. | \begin{align*}a > b\end{align*} | One solution |
How do you solve an ambiguous case problem?
The Ambiguous Case of the Law of Sines
- See if you are given two sides and the angle not in between (SSA).
- Find the value of the unknown angle.
- Once you find the value of your angle, subtract it from 180° to find the possible second angle.
- Add the new angle to the original angle.
What is ASA case?
“ASA” means “Angle, Side, Angle” “ASA” is when we know two angles and a side between the angles. To solve an ASA Triangle. find the third angle using the three angles add to 180° then use The Law of Sines to find each of the other two sides.
How many possible triangles can be formed?
How do you know if a triangle exists?
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 find the ambiguous case of the law of sines?
The Ambiguous Case of the Law of Sines 1 See if you are given two sides and the angle not in between (SSA). This is the situation that may have 2 possible answers. 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 know if a case is ambiguous?
When you are given two sides and an angle not in between those sides, you need to be on the lookout for the ambiguous case. 1. See if you are given two sides and the angle not in between (SSA). This is the situation that may have 2 possible answers.
How many possible M ∠ B for a triangle?
Check to see if the Quadrant II angle is a possible angle measurement for the triangle, using the sum of the angles of a triangle. Answer: In this case, there is only 1 possible m ∠ B , because there is only 1 possible triangle. To keep practicing similar problems, just scroll to the next one.
How to find the measure of ∠ C in triangle 1?
The best way to see this ambiguity is to solve a problem using the Law of Sines like normal… and, at the end..you’ll notice something. Use the law of sines to find the measure of ∠ c in triangle 1 below. Round your answer to the nearest whole number. Triangle 1
