Q2 of 45 Page 137

From the top of a lighthouse, an observer looking at a ship makes angle of depression of 60°. If the height of the lighthouse is 90 metre, then find how far the ship is from the lighthouse. (√3 = 1.73)


Let PQ be a light house of height 80 cm such that PQ = 90 m


And R be a ship.


Angle of depression from P to ship R = ∠BPR = 60°


Also, ∠PRQ(say θ) = ∠BPR = 60° [Alternate Angles]


Clearly, PQR is a right-angled triangle.


Now, In ∆PQR






⇒ QR = 30(1.73)


⇒ QR = 51.90 m


Hence, Ship is 51.90 m away from the light house.


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