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Question

From top of a tower the angle of depression of top and bottom of a multistored building are 30o and 60o respectively. If the height of the building is 100m. find the height if a tower.

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Solution

Let AB=height of the building=100m
DE=AC=AB+BC=h= height of the tower
ADC=60
BDC=60
Now
tan30=CBCD=xd
13=xd (1)
tan60=CACD=x+100d
3=x+100d (2)
From (1)
d=3x (3)
Substituting (3) in (2)
3=(x+100)3x
3x=x+100
2x=100
x=50
Height of the tower=DE=h=AB+CB=100m+x=100m+50m=150m


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