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The angle of depression of the top and bottom of a tower as seen from the top of a 100m high cliff are 30 degree and 60 degree respectively. Find the height of the tower. |
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Answer» Answer: In fig, HEIGHT of the cliff is AD = 100m height of the TOWER is CE Tan60°=AD/ED √3=100/ED ED√3=100 ED=100/√3 =100×√3/√3×√3(since denominator should not be irrational) =100√3/3 Tan 30°=AB/CB, (CB=ED) 1/√3=AB/100√3/3 On cross multiplying ,we get.. 100√3/3=AB√3 AB=100√3/3×√3 = 33.3m We KNOW that, CE= BD BD=AD - AB =100 -33.3 =66.67m=CE Therefore,height of the tower is 66.67 m. |
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