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A day full of math games & activities. Find one near you.

# A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree

**Solution:**

- Height of the tree = AB + AC
- Trigonometric ratio which involves AB, BC and ∠C is tan θ, where AB can be measured.
- Trigonometric ratio which involves AB, AC and ∠C is sin θ, where AC can be measured.
- Distance between the foot of the tree to the point where the top touches the ground = BC = 8 m

In triangle ABC,

tan C = AB / BC

tan 30° = AB / 8

1/√3 = AB / 8

AB = 8 / √3

sin C = AB / AC

sin 30^{°} = (8/√3) / AC

1/2 = 8/√3 × 1 / AC

AC = 8/√3 × 2

AC = 16 / √3

Height of tree = AB + AC

= 8/√3 + 16/√3

= 24/√3

= 24 × √3 / √3 × √3. [On rationalizing ]

= (24√3) / 3

= 8√3

So, the height of tree is 8√3 meters.

**☛ Check: **NCERT Solutions Class 10 Maths Chapter 9

**Video Solution:**

## A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.

Maths NCERT Solutions Class 10 Chapter 9 Exercise 9.1 Question 2

**Summary:**

If a tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it and the distance between the foot of the tree to the point where the top touches the ground is 8 m, then the height of the tree is 8√3 m.

**☛ Related Questions:**

- A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of 1.5 m, and is inclined at an angle of 30° to the ground, whereas for elder children she wants to have a steep slide at a height of 3m and inclined at an angle of 60° to the ground. What should be the length of the slide in each case?
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