Answer:
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°.
