What is the ambiguous case and why could it have two 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!
How do you know if a SSA triangle has two solutions?
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. 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 many solutions can the ambiguous case have?
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….Possible Triangles with SSA.
| If: | Then: | |
|---|---|---|
| iii. | \begin{align*}a > b \sin A\end{align*} | Two solutions |
| b. | \begin{align*}a = b\end{align*} | One solution |
What is the ambiguous case of the Law 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, no such triangle exists.
How do you solve SSA ambiguous triangles?
Solving SSA Triangles
- use The Law of Sines first to calculate one of the other two angles;
- then use the three angles add to 180° to find the other angle;
- finally use The Law of Sines again to find the unknown side.
Is there an SSA congruence?
In other words, congruence through SSA is invalid. A pair of sides and the included angle will uniquely determine a triangle. In other words, congruence through SAS is valid.
Does SSA prove congruence?
An SSA congruence theorem does exist. can be used to prove triangles congruent. sides and the corresponding nonincluded angle of the other, then the triangles are congruent.
How do you solve the SSA amous case?
How do you solve ambiguous problems?
As you read these consider how well you perform against these.
- Suppress your urge to control things.
- Learn to act without the complete picture.
- Understand that some of your decisions will be wrong.
- Work on your flexibility.
- Learn to deal with uncertainty.
- Realize there is not a defined plan you need to follow.
What is SSA triangle?
SSA stands for side – side – angle, and it means a triangle with known lengths of two sides and one known angle that is not between the two sides.
Is SSA a congruence theorem?
An SSA congruence theorem does exist. sides and the corresponding nonincluded angle of the other, then the triangles are congruent. That is, the SSA condition guarantees con. gruence if the angles indicated by the A are right or obtuse.
Does SSA prove similarity?
Are the triangles similar? Explain. While two pairs of sides are proportional and one pair of angles are congruent, the angles are not the included angles. This is SSA, which is not a similarity criterion.
What are the rules for ambiguous case SSA?
Lesson Ambiguous case SSA. Rules about the number of solutions. If the two given sides are equal in measure, the triangle is isosceles, and the other two equal angles can easily be found and we have a case of ASA. If the given side which is opposite the given angle is greater than the other given side, there is one solution.
When to use the law of sines in the ambiguous case?
As listed below. 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
Which is the best summary of the ambiguous case?
Summary of Ambiguous Case. In the chart below, the ambiguous case is summarized. The given angle can be either acute or obtuse (if the angle is right, then you can simply use right triangle solving techniques). The side opposite the given angle is either greater than, equal to, or less than the other given side.
Which is the correct way to solve a SSA triangle?
“SSA” means “Side, Side, Angle”. “SSA” is when we know two sides and an angle that is not the angle between the sides. To solve an SSA triangle. use The Law of Sines first to calculate one of the other two angles; then use the three angles add to 180° to find the other angle;
