Mathematics
As observed from the top of a 80 m tall lighthouse, the angles of depression of two ships, on the same side of a light house in a horizontal line with its base, are 30° and 40° respectively. Find the distance between two ships. Give your answer correct to nearest metre.
Heights & Distances
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Answer
As, alternate angles are equal.
∴ ∠BCA = ∠EBC = 30° and ∠BDA = ∠EBD = 40°.
Let AB be the lighthouse.
In △ABC,
In △ABD,
From figure,
CD = AC - AD = 138.56 - 95.24 = 43.32 ≈ 43 m.
Hence, distance between two ships = 43 m.
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