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A straight tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle of 60° with the ground. The distance from the foot of the tree to the point, where the top point touches the ground is 15 m. Find the ratio between total height of the tree and the distance from foot of the tree to top point of the tree.

A straight tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle of 60° with the ground. The distance from the foot of the tree to the point, where the top point touches the ground is 15 m. Find the ratio between total height of the tree and the distance from foot of the tree to top point of the tree. Correct Answer (2 + √3) ∶ 1

Given:

Angle of elevation = 60°

Distance from the foot of the tree to the point, where the top point touches ground = 15 m

Concept used:

tanθ = P/B

cosθ = B/H

P → Perpendicular

B → Base

H → Hypotenuse

Calculations:

In, ΔABC

tan60° = AB/BC

⇒ AB = 15√3

Cos60° = BC/AC

⇒ 1/2 = 15/AC

⇒ AC = 30

Total height of the tree = AB + AC = 15√3 + 30

⇒ 15(√3 + 2)

The ratio between total height of the tree and the distance from foot of the tree to top point of the tree = 15(√3 + 2) ∶ 15

⇒ (√3 + 2) ∶ 1

∴ The required ratio is (√3 + 2) ∶ 1

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