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The upper part of a tree is broken over by the strong wind makes an angle of $30 °$ with the ground. The top of the broken tree meets the ground at a distance of 25 m from the foot of the tree. What is the original height of the tree?

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253 + 50 3

253 m

203 m

answer is C.

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Detailed Solution

Given that,
The angle made by the upper part of the tree with the ground=

30 °

The distance between the top part of the broken tree that meets the ground and the foot of the tree=25m
We draw a right-angled triangle,
Question Image

In,

Δ A B C

,
Broken part of the tree = AB,
The unbroken part of the tree

A C = h

Distance between root and top of the tree

B C = 25 m

Substituting the values of

θ = 30 °

, AC and BC in

tan θ = A C B C

⇒ tan 30 ° = h 25 ⇒ h = 25 × 13 [∵ tan 30 ° = 13] ⇒ h = 253 .......1)

Substituting the values of

θ = 30 °

, AC and AB in

sin θ = A C A B

⇒ sin 30 ° = h A B ⇒ 12 × A B = 253 [∵ sin 30 ° = 12, h = 253] ⇒ A B = 503 ........2)

We get the height of the tree by adding equations (1) and (2),
Height of the tree= broken part + unbroken part

⇒ h = 503 + 253 ⇒ h = 25 + 50 3 ⇒ h = 753 ⇒ h = 253 m

Thus, the height of the tree will be

253 m

.
Therefore the correct option is 3.

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