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

Asked by maham237 @ in Mathematics viewed by 413 People

Answered by maham237 @


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
Answer:
The given measurements determine one triangle.

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