a vertical tower stands on a horizontal plane and is surmounted by a vertical flag staff of height h . At a height on the plane ,the angle of elevation of the bottom and the top of the flag staff are
and
respectively. Prove that the height of the tower is h tan a
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Answer:
Let height be y ΔOAC
tanθ=
B
P
tanβ=
OA
CA
tanβ=
x
y+h (y+h)→ Let AB, AB+BC
Let OA→ x
x=[
tanβ
y+x
]
Consider ΔOAB
tanα=
x
y
=
Base
perpendicular
x=
tanα
y
tanα
y
=
tanβ
y+h
ytanβ=tanαy+tanαh
ytanβ−tany=tanαh
y(tanβ−tanα)=tanαh
y=
tanβ−tanα
htanα
This proved.
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