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Use the Law of Sines to solve (if possible) the triangle for the value of c.

A = 27.5°, a = 15.0 cm, b = 36.4 cm

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Richard P. | Fairfax County Tutor for HS Math and ScienceFairfax County Tutor for HS Math and Sci...
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According to the law of sines,     a/sin(A) =  b/sin(B),   plugging in the values:
15/sin(27.5) = 36.4/sin(B)    One can rearrange this to be
sin(B) = (36.4/15) sin(27.5) =  1.12   
Of course this is not possible because the sine function cannot be greater than 1.
So there is no triangle with the values of length and angle given.  
It is not possible to solve.