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From a point on the edge of the sea ,one ship is 5km away on a bearing S50°E and another is 2km away on a bearing S60°W.
How far apart are the ships

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Answer :

olumideolawoyin

Answer:

5.99km

Step-by-step explanation:

Please find the attached.

View image olumideolawoyin
mhanifa

5.99 km

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Let's denote the point on the edge of the sea as point A, the position of the first ship as point B, and the position of the second ship as point C.

According to the bearings given:

  • Ship B is 5 km away on a bearing S50°E.
  • Ship C is 2 km away on a bearing S60°W.

First, let's calculate the angle BAC between the two bearings.

The total angle between the bearings is:

  • 50° + 60° = 110°

Using the Law of Cosines:

  • d² = a² + b² - 2ab * cos(θ)

Substituting the values:

  • d² = 5² + 2² - 2 * 5 * 2 * cos(110°) ≈ 35.84

Taking the square root of 35.84:

  • d ≈ 5.99 km

So, the ships are approximately 5.99 km apart.

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