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prefer to it child
Step-by-step explanation:
Let BC be the tower and CD be the flagstaff.
The angle of elevation of the bottom of the flagstaff is α and that of the top of flagstaff is β.
Let h be the height of the tower
In △ABC, we have
⇒tanα=
AB
BC
....{i}
In △ABD
⇒tanβ=
AB
BD
⇒
AB
BC+h
=
AB
BD
....{ii}
Now dividing {ii} by {i}, we get
BC
BC+h
=
tanα
tanβ
⇒(BC+h)tanα=BCtanβ
⇒BC(tanβ−tanα)=htanα
⇒BC=
tanβ−tanα
htanα
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