For a bird flying at a height of 20\(\sqrt {3}\) m, the angle of depression to the top of a tree and the bottom of the tree at a particular moment is 30° and 60° respectively. What is the height of the tree?
Answer & explanation
Correct answer: option 2
Let E is the bird and AB is the tree.
In ΔEBC → Tan 60° = \(\frac{CE}{BC}\)
\(\sqrt {3}\) = \(\frac{20}{\sqrt {3}}\)
BC = 20
In ΔAED → Tan 30° = \(\frac{ED}{AD}\)
\(\frac{1}{\sqrt {3}}\) = \(\frac{ED}{20}\) [AD = BC]
ED = \(\frac{20}{\sqrt {3}}\)
Height of the tree = EC - ED = 20\(\sqrt {3}\) - \(\frac{20}{\sqrt {3}}\) = \(\frac{40}{\sqrt {3}}\)