In a violent storm, a tree got bent by the wind. The top of the tree meet the ground at an angle of 30˚, at a distance of 30 metres from the root. At what height from the bottom did the tree get bent? What was the original height of the tree?
Let AB be a tree, and P be the point of break,
And As tree falls, we can consider the situation as a right angled triangle at B
Given,
Angle of broken tree with ground, θ = 30°
Distance of top of broken tree from root, AB = 30 m
In ΔAPB
So, tree bents at a height of meters from the ground.
Also, In Δ APB
On cross – multiplying
AP = 10√3 × 2 = 20√3 meters
Original height of tree = AP + BP
= 20√3 + 10√3
= 30√3 meters