The angle of elevation of the top of a tower from certain point is 30. If the observer moves 20m towards the tower, the angle of elevation of the top increases by 15. Find the height of the tower. A) 3 m b) 53 m c) 103 m d) 203 m
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let us take two triangle ∆ABC(30°)&∆ABD(45°)
let AB be,Xmeter & height be h.
in∆ABC.
tan30°=P/B
1/√3=h/x
X=h√3...............(1)
in∆ABD.
tan45°=P/B
1=h/x+20
x=h-20.
from(1)&(2).
h√3=h-20.
20=h(1-√3)
h=20/1-√3
h=10(1-√3).
h√3=
let AB be,Xmeter & height be h.
in∆ABC.
tan30°=P/B
1/√3=h/x
X=h√3...............(1)
in∆ABD.
tan45°=P/B
1=h/x+20
x=h-20.
from(1)&(2).
h√3=h-20.
20=h(1-√3)
h=20/1-√3
h=10(1-√3).
h√3=
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