To approximate the area of a lake, a surveyor walks around

Chapter 8, Problem 40

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QUESTION:

To approximate the area of a lake, a surveyor walks around the perimeter of the lake, taking the measurements shown in the illustration. Using this technique, what is the approximate area of the lake? [Hint: Use the Law of Cosines on the three triangles shown and then find the sum of their areas.]

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QUESTION:

To approximate the area of a lake, a surveyor walks around the perimeter of the lake, taking the measurements shown in the illustration. Using this technique, what is the approximate area of the lake? [Hint: Use the Law of Cosines on the three triangles shown and then find the sum of their areas.]

ANSWER:


First, use the Law of Cosines to calculate the angle values for each triangle:
Triangle A: angle A = 90°, angle B = 66.7°, angle C = 23.3°
Triangle B: angle A = 23.3°, angle B = 63°, angle C = 93.7°
Triangle C: angle A = 93.7°, angle B = 66.

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