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
1√3=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