Question

A tree is broken at a height of 4m from the ground. Its top touches the ground at

a distance of 3m from the base of the tree. Find the original height of the tree.​

Answer 1

Given :

• Height of the tree (Broken) = 4 m

• Base distance = 3 m

To find :

The original height of the tree.

Solution :

Since the tree was broken at a certain Height , the part of the tree which fell at the ground will be the other part of the tree .

When we will sum of the broken part and the height of the tree will give us the orginal height of the tree.

According to the given information , the figure is resembling a Right-angled triangle.

And in the figure , we can see that AB is the height of the triangle , BC is the Base of the triangle and AC is the Hypotenuse of the triangle.

Here, we are provided with the base and height.

Hence we can use the Pythagoras theorem to determine the length of Hypotenuse (AC).

Pythagoras theorem :

$\boxed{\bf{H^{2} = P^{2} + B^{2}}}$

Where :

• H = Hypotenuse
• B = Base
• P = Height

Now using the Pythagoras theorem and substituting the values in it, we get :

$:\implies \bf{H^{2} = P^{2} + B^{2}}$

$:\implies \bf{AC^{2} = AB^{2} + BC^{2}}$

$:\implies \bf{AC^{2} = 4^{2} + 3^{2}}$

$:\implies \bf{AC = \sqrt{4^{2} + 3^{2}}}$

$:\implies \bf{AC = \sqrt{16 + 9}}$

$:\implies \bf{AC = \sqrt{25}}$

$:\implies \bf{AC = 5}$

$\boxed{\therefore \bf{AC = 5}}$

Hence the Hypotenuse/length of AC is 5 m.

To find the original height of the tree :.

According to the given information we are provided that :-

AB(Height) + AC(Hypotenuse) = Original height of the tree.

Let the original height of the tree be x m.

Now by substituting the values of AB and AC in the above equation , we get :

➝ 5 + 4 = x

➝ 9 m = x

Hence the original height of the tree is 9 m.

Answer 2

QuestioN :-

A tree is broken at a height of 4m from the ground. Its top touches the ground at a distance of 3m from the base of the tree. Find the original height of the tree.

ANsWeR :-

Given :-

Height of the broken tree = 4m

Base of the tree from top to bottom = 3m

To find :-

Original height of the tree

ANsWeR :-

By Pythagoras theorem ,

In ∆ ABC ,

AC = ?

BC = 4m

AB = 3m

So,

(AC)² = (AB)² + (BC)²

(AC)² = 3² + 4²

(AC)² = 9 + 16

(AC)² = 25

AC = √25

AC = 5m

Now, original height of tree ,

=> AC + CB = 5 + 4 = 9m

Hence , original height of tree is 9m