Question

4. A surveying team needs to measure the distance across the lake. They make the measurements shown along the ground. What is the distance across the lake?
If necessary, round your answer to the nearest tenth.

Answer 1

Applying the Law of Cosines, the distance across the lake is: 2.1 miles.

What is the Law of Cosines?

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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