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.
Answer & explanation
Correct answer: option 1
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