A straight tree is broken due to thunder storm. The broken part is bent in such a way that the peak of the tree touches the ground at an angle of 60 degree at a distance of 2root3m. Find the initial height of the tree.
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Answer:
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Given:
A straight tree is broken due to a thunderstorm.
The broken part is bent in such a way that the peak of the tree touches the ground at an angle of 60°.
The distance between the top and the base = 2√3m
To Find:
The initial height of the tree
Solution:
The initial height of the tree is 2 (3 + 2√3) m.
When the tree falls as shown in the diagram, a right-angled triangle is formed.
Let the name of the triangle be ΔABC with ∠B = 90°.
Since given that ∠C = 60° and the distance BC = 2√3m,
We can use trigonometric equations to find the remaining sides AB and AC.
In ΔABC,
tan C = AB / BC
or tan 60° = AB / BC
or √3 = AB / 2√3
or AB = 2 X √3 X √3
= 6m
Similarly,
cos C = BC / AC
or cos 60° = 2√3 / AC
or 1/2 = 2√3 / AC
or AC = 4 √3
The initial height of the tree is AB + AC = 6 + 4 √3
= 2 (3 + 2√3) m
