Class 10

Math

All topics

Some Applications of Trigonometry

The angle of elevation of the top of a vertical tower from a point on the ground is $60_{0}$ . from another point 10 m vertically above the first, its angle of elevation is$45_{0}$ .Find the height of the tower.

R.E.F. Image.

Height of the tower, H = (h+10)m

In $△ABC,$

$tan60_{∘}=ABh+10 $

$AB=3 h+10 ⋯(i)$

In $△DCO,$

$tan45_{∘}=ABh $

$∴AB=h⋯(ii)$

comparing eq.(i) and (ii), we get :

$h=3 h+10 $

$∴3 h=h+10$

$⇒3 h−h=10$

$⇒h(3 −1)=10$

$∴h=3 −110 $

Height of tower = h + 10

$=3 −110 +10$

$=3 −110+103 −10 $

$H=3 −1103 m$