Lighthouse B is 9 miles west of lighthouse A. A boat leaves A and sails 4 miles. At this​ time, it is sighted from B. If the bearing of the

Question

Lighthouse B is 9 miles west of lighthouse A. A boat leaves A and sails 4 miles. At this​ time, it is sighted from B. If the bearing of the boat from B is N​E65, how far from B is the​ boat?

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Vân Khánh 4 years 2021-07-18T10:44:03+00:00 1 Answers 11 views 0

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  1. Euphemia
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    2021-07-18T10:45:40+00:00
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    Answer:

    The distance of the boat from B is approximately 9.4 miles

    Step-by-step explanation:

    The location of light house B from A = 9 miles west

    The distance of the boat from A = 4 miles

    The bearing of the boat from A = NE65

    We have;

    4/(sin25) = 9/sin(B)

    sin B = 9*sin(25)/4

    B ≈ 71.969

    a² = 4² + 9² – 2 × 4 × 9 × cos(180 – 25 – 71.969) ≈ 88.264

    The distance of the boat from B, a ≈ √88.264 ≈ 9.4

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