Q10 of 45 Page 138

While landing at an airport, a pilot made an angle of depression of 20°. Average speed of the plane was 200 km/hr. The plane reached the ground after 54 seconds. Find the height at which the plane was when it started landing. (sin 20° = 0.342)


Let the initial position of plain be P and after landing it position be R.


Now,


Angle of depression while landing, ∠CPR = 20°


Also, ∠ CPR = ∠PRQ (say θ) = 20° [Alternate Angles]


Now,


Speed of plane = 200 km / hr



Time taken for landing = 54 seconds


Distance travelled in landing = PR


Also, distance = speed × time



Now, In ∆PQR




⇒ PQ = 3000 × sin 20°


⇒ PQ = 3000(0.342)


⇒ PQ = 1026 m


So, Plane was at a height of 1026 m at the start of landing.


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