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To get to a park, a tourist goes by car from his house 31 Km heading S67°W, he goes 12 Km heading S11°W for getting to the park. Calculate the distance on straight line from his house to the park. Round your answer to one decimal.

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sqdancefan

Answer:

  39.0 km

Step-by-step explanation:

The straight-line distance from the house to the park can be found using the Law of Cosines. The angle where the tourist turned is (180° -(67° -11°)) = 124°. The formula is ...

  c = √(a² +b² -2ab·cos(C))

  c = √(31² +12² -2(31)(12)cos(124°)) ≈ √1521.0395

  c ≈ 39.00

The straight-line distance from the house to the park is 39 km.

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