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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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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