Question

A vertical tree is broken by wind such that its top touches the ground at 30 m away from its foot and makes 30° angle from the ground. Find the height of tree before broken.

Answer 1

Given: The top of a vertical tree touches the ground 30 m from its foot and the broken top makes a 30° angle with the ground. Let the tree’s original height = H, the height of the remaining standing part = BC = x and the fallen part = AC = H – x.

Step-wise calculation:

1. In right triangle ABC, right angle at B, AB = 30 m and ∠BAC = 30°.

2. AC is the hypotenuse.

So, `AC = (AB)/(cos 30^circ)` 

= `30/(sqrt(3)/2)`

= `60/sqrt(3)` 

= `20sqrt(3)` m

3. BC = AC × sin30°

= `20sqrt(3) xx 1/2` 

= `10sqrt(3)` m

4. Original height

H = BC + CD 

= BC + AC

= `10sqrt(3) + 20sqrt(3)` 

= `30sqrt(3)` m

5. Numerical value:

`30sqrt(3) ≈ 51.96` m

The tree’s height before it was broken was `30sqrt(3)` m (≈ 51.96 m).