Q7 of 45 Page 138

From the top of the light house, an observer looks at a ship and finds the angle of depression to be 30°. If the height of the light-house is 100 meters, then find how far the ship is from the light-house.


Let PQ be a light house of height 80 cm such that PQ = 100 m


And R be a ship.


Angle of depression from P to ship R = ∠BPR = 30°


Also, ∠PRQ(say θ) = ∠BPR = 30° [Alternate Angles]


Clearly, PQR is a right-angled triangle.


Now, In ∆PQR





⇒ QR = 100√3 m


Hence, Ship is 100√3 m away from the light house.


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