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


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