math-law of sins

solve the triangle:
1. A= 61 degrees
a=8
b=21

2. A=136 degrees
a=15
b=28

3. C=115 degrees
b=12
c=7

For all of these problems I used law of sins and when I input it into my calculator I get domain error after doing sin inverse to get an angle degree. What am I doing wrong?

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  1. These problems are made up to show some cases where the triangle cannot exist.

    If A=61° (acute) and a=8, the longest side adjacent to A is a/sin(61°)=9.15.
    Since 21>>9.15, the triangle does not exist.

    If A is obtuse, then any adjacent side must be less than a.

    Verify the above with a few triangles.

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  2. Okay, so all three of these are cases where the triangle does not exist?

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  3. I suggest you
    1. verify if the triangles exist or not according to the two (different) conditions above.
    2. try to draw the given triangle, if possible.

    If you have doubts, you are welcome to post your answers/results for a check.

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