Question

A tree is broken by the wind. The top struck the ground at an angle of 30° and at a distance 30 m from the root. Find the whole height of the tree. (`sqrt(3)`=1.73)

Answer 1

Let AB represent the height of the tree.

Let the tree break at point C.

AC is the broken part of the which takes position CD such that ∠CDB = 30° 

∴ Ac = CD                   ....(1)

In right-angled ΔCBD,

tan 30° = `(BC)/(BD)`

∴`1/sqrt(3) = (BC)/30`

∴ BC = `30/sqrt(3)`

 cos 30°  = `(BD)/(CD)`

∴ `sqrt(3)/2 = 30/(CD)`

∴ `sqrt(3) xx CD = 30  xx2 `

∴CD `60/sqrt3`

 Ab = AC + BC                                         .....[A-C-B]

∴ AB = CD + BC                                      ... [From (i)] 

∴ AB =`60/sqrt3 + 30/ sqrt 3`

∴ AB = `90/sqrt3 = 90/ sqrt3 xx sqrt3/ sqrt3`         ....[Rationalizing the denominator]

∴ AB `(90sqrt3)/3 = 30sqrt3 = 30 xx 1.73 = 51.9` m

∴ Height of the tree is 51.9 m.