Applying the law of cosine, b² = a² + c² - 2ac(cos B), the length of AC of the marsh, to one decimal place, is: 522.1 meters
<h3>What is the Law of Cosine?</h3>The Law of Cosine is given as, b² = a² + c² - 2ac(cos B).
From the diagram given, we have the following:
- B = 180 - 75 = 105°
- b = AC (length of the marsh)
- a = 220 m
- c = 420 m
Plug in the values into the law of cosine formula:
b² = 220² + 420² - 2(220)(420)(cos 105)
b² = 272,629.8
b = √272,629.8
b = 522.1 meters. (Length of AC of the marsh)
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