Question 621829: How many distinct triangles can be formed if a=12, b=9, and angle A= 38degrees? please add detail on how to find the correct answer!
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website!
This is the AMBIGUOUS case SSA, (side-side-angle)
Rules about the number of solutions.
1. 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.
2. If the given side which is opposite the given angle is greater
than the other given side, there is one solution.
3. If the given side which is opposite the given angle is shorter
than the other given side, then we calculate the product of the longer
given side times the cosine of the given angle. If the shorter given
side is shorter than this number, then the shorter given side is too
short to form a triangle and there is no solution. Otherwise there are
two solutions.
Your problem is a=12, b=9, and angle A = 38°.
That's case 2. The given side which is opposite the given angle A is a=12,
which is greater than the other given side, b=9 so there is one solution.
Edwin
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