A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30 with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.

Explanation

Let the Height of the Tree =A B+A D

and given that {BD}=8 {m}

Now, when it breaks a part of it will remain perpendicular to the ground (A B) and remaining part ({AD}) will make an angle of `30^{circ}`

Now, in triangle {ABD}

`cos 30^{circ}=frac{{BD}}{{AD}} ``Rightarrow {BD}=frac{sqrt{3} {AD}}{2}`` Rightarrow {AD}=frac{2 times 8}{sqrt{3}}`

also, in the same Triangle

`tan 30^{circ}=frac{{AB}}{{BD}}`` Rightarrow {AB}=frac{8}{sqrt{3}}`

therefore Height of tree ={AB}+{AD}`=(frac{16}{sqrt{3}}+frac{8}{sqrt{3}}right) {m}=frac{24}{sqrt{3}} {~m}=8 sqrt{3} {~m}`