Answer:
To find the smallest angle, we'll use the cosine rule formula. Let c = 300,b= 200,a = 250
<A is the angle facing side a. <B is the angle facing side b. <C is the angle facing side c.
a² = b² + c² - 2bc.cosA
250² = 200² + 300² - 2*200*300.cosA
62,500=40,000+90,000-120,000.cosA
62,500=130,000-120,000.cosA
120,000.cosA=130,000-62,500
120,000.cosA=67,500
cosA = 0.5625
<A = 55.8°
b² = a² + c² - 2ac.cosB
40,000=62,500+90,000-2*250*300.cosB
40,000=152,500-150,000.cosB
150,000.cosB=152,500 - 40,000
150,000.cosB=112,500
cosB = 0.75
<B = 41.4°
c² = a² + b² - 2ab.cosC
90,000=62,500+40,000-2*250*200.cosC
90,000=102,500-100,000.cosC
100,000.cosC=102,500-90,000
100,000.cosC=12,500
cosC = 0.125
<C = 82.8°
Therefore the smallest angle is <B which is 41.4°.