The sides of a triangle measure 14.9 cm, 23.8 cm, and 36.9 cm. find the measure of the angle with the least measure.

You can make use of the law of cosines.
a² = b² + c² - 2bc·cos(A)
Solving for the angle, you have
A = arccos((b²+c²-a²)/(2bc))

Substituting the given values gives you
A = arccos((23.8²+36.9²-14.9²)/(2·23.8·36.9))
A = arccos(1706.04/1756.44)
A ≈ arccos(0.9713056)
A ≈ 13.75879° ≈ 13.8°

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It can also be convenient to use a triangle solver. This one gives the same result: 13.8°.