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Find the height of the tree. If a tree breaks due to a storm and the broken part bends in such a way the top of the tree touches the ground making an angle 45° with the ground and the distance between the foot of the tree to where the top touches the ground is 20 m.

Find the height of the tree. If a tree breaks due to a storm and the broken part bends in such a way the top of the tree touches the ground making an angle 45° with the ground and the distance between the foot of the tree to where the top touches the ground is 20 m. Correct Answer 20(1 + √2) m

From the figure,

Height of the Tree = BC + BD

In triangle BCD

⇒ tan 45° = Perpendicular/Base  = BC/CD

⇒ tan 4

5° = BC/20

⇒ BC = 20

We use Pythagoras theorem,

⇒ BD2 = BC2 + CD2

⇒ BD2 = 202 + 202

⇒ BD = 20√2

∴ Height of the tree = 20 + 20√2 = 20(1 + √2) m

Alternate solution:

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From the figure,

Height of the tree = x + √2x

⇒ x = 20

⇒ √2x = 20√2

∴ Height of the tree = 20(1 + √2) m 

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