The angle of elevation of top of a tree from a point on the ground which is 105 m away from the base of the tree is 30°. When the height of the tree increases, the angle of elevation changes to 45°. Find out the increase in the height of the tree.

35(3 - √3) m

BC = 105 m

Increase in height of tree = AD

In ΔABC, 

tan 30°  =        1      :       \(\sqrt {3}\)

                     (AB)          (BC)

                       ↓                ↓

                       ↓              105

             \(\frac{105}{\sqrt {3}}\) = \(\frac{105}{3}\) \(\sqrt {3}\) = 35 \(\sqrt {3}\)

In ΔCBD, 

tan 45°  =        1      :       1

                     (BD)          (BC)

                       ↓                ↓

                     105            105

AD = DB - AB = 105 - 35 \(\sqrt {3}\) = 35 (3 - \(\sqrt {3}\)) m