State whether the given measurements determine zero, one, or two triangles. c = 30°, a = 28, c = 14

The given measurements determine one triangle.

Step-by-step explanation:

The Cosine Law:

c² = a² + b² - 2 a b cos C

14² = 28² + b² - 56 · b · √3/2

196 = 784 + b² - 28√3 b

b² - 28√3 b + 588 = 0

b 1/2 = (28√3 +/- √(2352 - 2352 )) / 2 = 28√3 / 2 = 14√3

The given measurements determine one triangle.