Q20 of 20 Page 9


A tower subtends an angle α at a point A in the place of its base and the angleof depression of the foot of the tower at a point b ft. just above A is β.Prove that the height of the tower is b tanα cotβ.


https://gs-post-images.grdp.co/user_files/63094/15047/images/extra-9_files/y57.gif


Let x be the distance of the point A from the foot of the tower and h be the height of the tower.


In Δ APQ,


h = x tanα …… (i)


In Δ PRB


b = x tanβ …… (ii)


From (i) and (ii),


h = b.tanα /tanβ

= b.tanα cotβ

Therefore the height of the tower is b tanα cotβ.

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