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A Storm Broke a Tree and the Treetop Rested 20 M from the Base of the Tree, Making an Angle of 60° with the Horizontal. Find the Height of the Tree. - Geometry

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Question

A storm broke a tree and the treetop rested 20 m from the base of the tree, making an angle of 60° with the horizontal. Find the height of the tree.

Solution

Let AC be the original height of the tree. Suppose BD be the broken part of the tree which is rested at D from the base of the tree. 
Here, CD = 20 m and ∠BDC = 60º.
In right ∆BCD,
\[\tan60^\circ = \frac{BC}{CD}\]
\[ \Rightarrow \sqrt{3} = \frac{BC}{20}\]
\[ \Rightarrow BC = 20\sqrt{3} m . . . . . \left( 1 \right)\]
Also,
\[\cos60^\circ = \frac{CD}{BD}\]
\[ \Rightarrow \frac{1}{2} = \frac{20}{BD}\]
\[ \Rightarrow BD = 40 m . . . . . \left( 2 \right)\]
∴ Height of the tree = AB + BC = BD + BC =
\[\left( 40 + 20\sqrt{3} \right) m\]               [Using (1) and (2)]
Thus, the height of the tree is \[\left( 40 + 20\sqrt{3} \right) m\]

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APPEARS IN

 Balbharati Solution for Balbharati Class 10 Mathematics 2 Geometry (2018 to Current)
Chapter 6: Trigonometry
Practice set 6.2 | Q: 5 | Page no. 137
Solution A Storm Broke a Tree and the Treetop Rested 20 M from the Base of the Tree, Making an Angle of 60° with the Horizontal. Find the Height of the Tree. Concept: Heights and Distances.
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