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A tree of height 15 m is broken by wind in such a way that its top touches the ground and makes an angle 30° with the ground. What is the height from the ground to the point where tree is broken?

A tree of height 15 m is broken by wind in such a way that its top touches the ground and makes an angle 30° with the ground. What is the height from the ground to the point where tree is broken? Correct Answer 5 m

Given:

Height = 15 m

Makes angle = 30° 

Formula Used:

sin θ = perpendicular/hypotenius

sin 30° = 1/2

Calculation:

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From the figure:

In triangle ABC:

Sin30° = AB/BC

⇒ 1/2 = AB/BC

⇒ BC = 2AB

Total height of the tree = AB + BC = 15 m

Hence, 3AB = 15

⇒ AB = 5 m

∴ The height from the ground to the point where tree is broken is 5 m

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