Question

A vertical tree is broken by the wind. The top of the tree touches the ground and makes an angle 30°with it. If the top of the touches the ground 30m away from its foot, then find the actual height of the tree.

Answer 1

Answer :

30√3 m

Solution :

• Let OA be the tree with O as foot and A as top .

• Let B be the point of break , such that OB = x and AB = y .

• Height of tree = OA = x + y

Now ,

In right angled triangle ∆OAB ,

OA = 30 m (given)

OB = x m

AB = y m

Thus ,

=> tan(∠OAB) = OB/OA

=> tan30° = x/30

=> 1/√3 = x/30

=> (1/√3) × 30 = x

=> x = 30/√3

=> x = 10√3

Also ,

=> cos(∠OAB) = OA/AB

=> cos30° = 30/y

=> √3/2 = 30/y

=> y = 30 × 2/√3

=> y = 20√3

Now ,

Actual height of the tree OA

= OB + AB

= x + y

= 10√3 + 20√3

= 30√3

Hence ,

Required answer is 30√3 m .

Answer 2

Answer:

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