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 do you know if it’s an ambiguous case?
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 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 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.
When to use the ambiguous case of sine law?
The Ambiguous Case of Sine Law ambiguous case:a problem that has two or more solutions Sine law Used when: i)two sides and an opposite angle are known ii)two angles and one side are known You must always consider the ambiguous case of sine when you have an oblique triangle with two sides and an opposite angle given.
Which is the ambiguous case in triangle solving?
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 an example of an ambiguous case?
The so-called ambiguous case arises from the fact that an acute angle and an obtuse angle have the same sine. If we had to solve x = 45° or x = 135°. ( Topic 4, Example 1 .) In the following example, we will see how this ambiguity could arise. In triangle ABC, angle A = 30°, side a = 1.5 cm, and side b = 2 cm.
What are the angles of a triangle according to the law of sines?
Let us call that side x. Now, according to the Law of Sines, in every triangle with those angles, the sides are in the ratio 643 : 966 : 906. Therefore, Problem 1. The three angles of a triangle are A = 30°, B = 70°, and C = 80°.