Applying the Law of Cosines, the distance across the lake is: 2.1 miles.
<h3>What is the Law of Cosines?</h3>Law of Cosines is given as: c² = a² + b² - 2(a)(b)cos(C).
The diagram showing the measurements along the ground is in the attachment below.
Given:
- a = 2.82 miles
- b = 3.11 miles
- C = 40.3°
- c = distance across the lake.
Applying the Law of Cosines, we have:
c² = 2.82² + 3.11² - 2(2.82)(3.11)cos(40.3)
c² = 4.25
c = √4.25
c = 2.1 miles
Thus, applying the Law of Cosines, the distance across the lake is: 2.1 miles.
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