In triangle abc a=2, c=3, b=95 degrees. find the size of the smallest angle

  A ≈ 32°

Step-by-step explanation:

You are given two sides and the angle between them, so the law of cosines applies. The measure of side b can be found to be ...

  b² = a² + c² -2ac·cos(B)

  b² = 2² +3² -2·2·3·cos(95°) ≈ 14.0459

  b ≈ 3.74778

Then the law of sines can help you find angle A, the angle opposite the shortest side.

  sin(A)/a = sin(B)/b

  A = arcsin(a/b·sin(B)) = arcsin(2/3.74778·sin(95°)) ≈ 32.11°

  A ≈ 32°

The smallest angle is about 32°.