A tree breaks due to storm and the broken part bends so that the top o

1.	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.
Answer» Answer Let AC be the broken part of the tree. ∴ Total height of the tree = AB+AC In right ΔABC, cos 30° = BC/AC ⇒ √3/2 = 8/AC ⇒ AC = 16/√3 Also, tan 30° = AB/BC ⇒ 1/√3 = AB/8 ⇒ AB = 8/√3 Total height of the tree = AB+AC = 16/√3 + 8/√3 = 24/√3

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.

Answer»

Answer

Let AC be the broken part of the tree.

∴ Total height of the tree = AB+AC

In right ΔABC,

cos 30° = BC/AC

⇒ √3/2 = 8/AC

⇒ AC = 16/√3

Also,

tan 30° = AB/BC

⇒ 1/√3 = AB/8

⇒ AB = 8/√3

Total height of the tree = AB+AC = 16/√3 + 8/√3 = 24/√3