From the top of lighthouse, an observer looks at a ship and finds the angle of depression to be 60∘. If the height of the lighthouse is 90 metres, then find how far is that ship from the lighthouse? (√3=1.7.3)
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Solution
Let AB=90m represents the height of lighthouse. Point C represents the position of the ship. Draw ray AM∥ seg BC ∠ACB is the angle of depression, ∠MAC=60o Also, ∠ACB≃∠MAC (Alernate angles) ∠ACB=60o Let the distance of ship from the light-house be x metres. In right angled ΔABC, tan60o=90x ⇒x=90√3×√3√3 =90√33 =30√3 =30×1.73=51.9 ∴ Distance of the ship from the lighthouse is 51.9m.