How do you determine the number of possible solutions, if any, using the rule for law of sines(ambiguous case) given A=35*, b=12, a=9.1?

1 Answer
Jim H
Aug 5, 2015

See explanation.

Explanation:

Find #sinB#

#sinB = (12sin(35^@))/9.1~~ 0.756365#

OK, that is less that or equal to #1#, so there is a solution.

#sin^-1(0.756365) ~~ 49.14^@#

So #B = 49.14^@# is one solution.
(And #C = 180 -(35+49.14)^@ = 95.86^@#)

Another angle with the same sine is #180^@ - 49.14^@ = 130.86^@#

Add the #35^@# angle we started with, to get: #165.86#.
We have not gone over the #180^@# total for the angles of a triangle, so #B = 130.86^@# will give us a second solution.
(And #C = 180 -(35+130.86)^@ = 14.14^@#)

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