Question

In the diagram below, points A and B represent two lakes. How far apart are the lakes? 131.5 ft 456.3 ft 474.6 ft 633.9 ft

Answer 1

Answer:

I don't know the answer, but I just took a test and the answers ARE NOT 456.3 and ARE ALSO NOT 474.6

Step-by-step explanation:

Answer 2

The distance between the two lakes = 633.9 ft. So, we take the 4th option.

What is the law of cosines?

By the law of cosines, a triangle with sides a, b, and c, and the angle opposite to c being γ,

c = √(a² + b² - 2.a.b.cos γ)

How do we solve the given question?

To solve the question, we will use the law of cosines.

Let a = 560 ft., b = 350 ft., c = d (unknown distance).

γ = 160° - 75° = 85°.

We substitute the values in the formula to get,

d = √(560² + 350² - 2(560)(350)(cos 85°)

or, d = √(313600 + 122500 - 392000*0.0871)

or, d = √(436100 - 34165.05116)

or, d = √401934.948842

or, d = 633.983397

So, we take d = 633.9 ft., the 4th option.

∴ The distance between the two lakes = 633.9 ft.

Learn more about the law of cosines at

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