Question

The top of a palm tree having been broken by the wind struck the ground at an angle of 60° at a distance of 9m from the foot of the tree. Find the original height of the palm tree. 

Answer 1

Let AC was original tree. It was broken into two parts. The broken part A' B is making 60° with ground.

In ΔA'BC

`"BC"/"A'C" = tan 60^circ`

`"BC"/9 = sqrt(3)`

`BC = 9sqrt(3)`

`"A'C"/"A'B" = cos 60^circ`

`9/"A'B" = 1/2`

`A'B = 18`

Height of tree = A'B + BC

= `9sqrt(3) + 18 = 9 × 1.732 + 18 = 15.588 + 18 = 33.588`

Hence , the height of tree was 33.588 m = 33.6 m (approximately).