Q25 of 31 Page 1

From the top of tower, 100 m high, a man observes two cars on the opposite sides of the tower with the angles of depression 30o& 45 o respectively. Find the distance between the cars. (Use √3=1.73).


Let us consider a tower AB, and the man observes two cars C and D on the opposite sides of the tower with angle of depressions 30° and 45° respectively.


Given


Height of tower, AB = 100 m


Angle of depression to car C, ∠PAC = ∠ACB = 30° [say θ1]


Angle of depression to car D, ∠QAD = ∠ADB = 45° [Say θ2]


To find: Distance between cars, CD


In ΔABC





⇒ BC = 100√3 m


In ΔABD





⇒ BD = 100 m


CD = BC + BD


⇒ CD = 100√3 + 100


⇒ CD = 100(1.73) + 100


⇒ CD = 173 + 100


⇒ CD = 273 m


Therefore, distance between cars is 273 m


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