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.
Let AC was the original tree. Due to storm, it was broken into two parts. The broken part A'B is making 30° with the ground.
BC/A'C = tan 30º
BC/8 = 1/ sqrt3
`BC = (8/sqrt3)m`
A'C'/A'B = cos 30º
`8/(A'B) = sqrt3/2`
`A'B = ((16)/sqrt3)m`
Height of tree = A'B+BC
`=(16/sqrt3+8/sqrt3)m = 24/sqrt3 m`
Hence the height of the tree is `8sqrt3 m`