SOLUTION: If you are given values for two sides of an oblique triangle and an angle opposite one of them, how would you arrive at the values of the missing parts? Will this result in a uniqu

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Question 67533: If you are given values for two sides of an oblique triangle and an angle opposite one of them, how would you arrive at the values of the missing parts? Will this result in a unique triangle?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Given the values of two sides of an oblique triangle ABC (one that does not contain a right angle) and an angle opposite one of them, how would you find the values of the missing parts?
Assume that we are given sides a and b and angle A
There are three cases to consider in this situation:
1. If angle A is acute and the length of side a lies between b and b sin A, then there will be two soltions.
2. If angle A is acute and the length of a < b sin A, or if if angle A is obtuse and a < b or a = b, then there is no solution.
3. For all other cases, there is one solution.
Let's consider case 3. We will be applying the law of sines: a%2Fsin+A = b%2Fsin+B = c%2Fsin+C
To find angle B:
a%2Fsin+A+=+b%2Fsin+B Solve for sin B
sin+B+=+%28b+sin+A%29%2Fa
B+=+arcsin%28%28b+sin+A%29%2Fa%29
To find side c:
c%2Fsin+C+=+a%2Fsin+A Solvefor c.
c+=+%28a+sin+C%29%2Fsin+A