From the top of a building 90 m high, the angles of depression

From the top of a building 90 m high, the angles of depression of the top and the bottom of a tree are 30° and 45° respectively. What is the height of the tree?

  1. 30√3 m
  2. 90 - 30√3 m
  3. 90 + 30√3 m
  4. 60 + 30√3 m

Answer

Let distance between the building and tree be d. Let the height of tree be h.

DE = d and CD = h

tan 45° = 90/d

1 = 90/d

d = 90

tan 30° = (90-h)/d

1/√3 = (90-h)/d

d = (90-h)√3

90/√3 = 90 - h

h = 90 - 90/√3

h = 90 - 30√3

The correct option is B.