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ICSE Class 10 Mathematics Question 39 of 49

Multiple-Choice Questions — Question 39

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Question 39

A man standing on a ship approaching the port towards the lighthouse is observing the top of the lighthouse. In 10 minutes, the angle of elevation of the top of the lighthouse changes from α to β. Then :

  1. α > β

  2. α < β

  3. α = β

  4. α ≤ β

Answer

Let A be the top of the lighthouse, C the initial position of ship and D be the position after 10 minutes.

A man standing on a ship approaching the port towards the lighthouse is observing the top of the lighthouse. In 10 minutes, the angle of elevation of the top of the lighthouse changes from α to β. Then : Maths Competency Focused Practice Questions Class 10 Solutions.

From figure,

tan α = ABBC\dfrac{AB}{BC}

tan β = ABBD\dfrac{AB}{BD}

Since, BC is greater than BD.

∴ tan α < tan β

⇒ α < β.

Hence, Option 2 is the correct option.