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The figure shows a 1175-yard-long sand beach and an oil platform in the ocean. The angle made with the platform from one end of the beach is 82”and from the other end is 75”Find the distance of the oil platform, to the nearest tenth of a yard, from each end of the beach.

User Dbgrman
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1 Answer

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Answer:

  • 2904.7 yards from "one end"
  • 2977.9 yards from "the other end"

Explanation:

You want the side lengths of a triangle with one angle of 82° and the other angle of 75° on either end of a side of length 1175 yards.

Sine law

The angle opposite the given side is ...

180° -82° -75° = 23°

The Law of Sines tells us the side lengths are proportional to the sine of the opposite angle. The middle-length side, opposite the 75° angle, has length ...

(1175 yd)·sin(75°)/sin(23°) ≈ 2904.7 yd . . . . from one end

The longest side, opposite the largest angle, is ...

(1175 yd)·sin(82°)/sin(23°) ≈ 2977.9 yd . . . . from the other end

The two distances to the platform are 2904.7 yd and 2977.9 yd.

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Additional comment

The platform is about 2876.4 yd from the beach.

We don't have the figure, so we have assumed an acute triangle in which each angle is measured between the platform and the other end of the beach.

Please hurry! The figure shows a 1175-yard-long sand beach and an oil platform in-example-1
User Chenny
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