The given measurements may or may not determine a triangle. if not, then state that no triangle is formed. if a triangle is formed, then use the law of sines to solve the triangle, if it is possible, or state that the law of sines cannot be used. b = 137°, c = 6, b = 11

If you're going to use technology (), you may as well use appropriate technology (a triangle solver). Many graphing calculators have this function built in.

a ≈ 5.82
A ≈ 21.2°
C ≈ 21.8°

Since the longest side (b) is opposite the given angle (B), the triangle has one solution.
.. C = arcsin(6/11*sin(137°))
.. A = 180° -137° -C
.. a = sin(A)*11/sin(137°)