Question: 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 to top touches the ground is 12 m then the height of the tree is-
Solution:
Let the height of the tree be h. Let the part that is still standing on the ground be x, and that part which has fallen be y.
Hence, we have
sin θ = x/y
⇒ sin θ = 1/2 ;[ θ = 30°]
⇒ x/y = 1/2
⇒ y = 2x ...............(1)
Also, it is given that the distance of the tip of the fallen tree to that of the base of the tree is 12 m
⇒ cos θ = 12/y
⇒ cos 30° = 12/y
⇒ √3/2 = 12/y
⇒ y = 24/√3 = (8 × √3 × √3)/√3
⇒ y = 8√3
From (1), x = 8√3/2 = 4√3
∴ Height of tree, h = x + y = 4√3 + 8√3 = 12√3 m