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In the triangle ABC, a = 14 , b = 10 and the measure of angle A = 150.

Now use the law of sines:

sin A / a = sin B / b

=> sin 150 / 14 = sin B / 10

=> sin B = (10/14)*sin 150

=> B = arc sin [(10/14)*sin 150]

=> B = 20.9248

For the sine function, sin (180 - x ) = sin x

The other value that B could have taken to satisfy the law of sines is that of 180 - 20.9248, which is not possible as the angles of a triangle add up to 180 degrees and A is given as 150.

**The maximum number of triangles that can have A = 150 , a = 14 and b = 10 is 1. **

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