. A tree breaks due to the storm and the broken part bends so that the top of
A tree breaks due to the storm and the broken part bends so that the top of the tree touches the ground making an angle of 30° with the ground. The distance from the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.
Let CBA be tree of height (h + x) m.
Let the height of the tree after broken part be h m
⇒ Let AB = BD = x and CD = 8 m [given]
In ∆BCD, CD/x = cos 30°
⇒ 8/x = √3/2
⇒ x = 16/√3 × √3/√3 = 16√3/3
In ∆BCD, h/8 = tan 30° = 1/√3
⇒ h = 8/√3 = 8/√3 × √3/√3 = 8√3/3
∴ Height of the tree
= h + x = 8√3/3 + 16√3/3 =24√3/3 = 8×1.73 = 13.83 m