Teaching this particular topic in the past has created numerous headaches for both me and my students. 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.
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. These possibilities are summarized in the diagrams below:. Suppose we are given side a, side b and angle A of triangle ABC. Answer: As listed below. 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 you have a SSA angle case with two possible solutions, how can you check both solutions to make sure they are correct?
How do you find the second triangle in the ambiguous case? Find the value of the unknown angle. If already one obtuse angle given, it can not have a second set of values. What is ambiguous case of triangle? Three different cases exist. If the side opposite the given angle is greater than the other given side, then exactly one triangle is determined.
These cases are illustrated below. 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. The chart shows how many triangles can be determined with each possibility, and the case numbers that we used in this section accompany each possibility.
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