Determine the maximum number of triangles possible when m∠A = 150, a = 14, and b = 10.
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.