A tall tree is broken by a storm. It broke at a point but did not separate. Its top touched the ground at a distance `40` m from its base. If the height of the point from the ground at which the tree broke is `9` m, find the height of tree before it was broken.

Answer

To find the height of the tree before it was broken, we can follow these steps:

1. **Understand the Problem**:
- We have a tree that is broken at point C and the top of the tree (point B) touches the ground at a distance of 40 m from the base (point A) of the tree.
- The height of the break point C from the ground is 9 m.

2. **Visualize the Situation**:
- Let A be the base of the tree, C be the point where the tree broke, and B be the top of the tree that touches the ground.
- We can visualize a right triangle formed by points A, C, and B.

3. **Identify the Right Triangle**:
- In triangle ABC:
- AC is the height of the tree before it was broken (which we want to find).
- CB is the length of the broken part of the tree that has fallen to the ground.
- AB is the distance from the base of the tree to the point where the top touches the ground, which is given as 40 m.

4. **Use the Pythagorean Theorem**:
- According to the Pythagorean theorem, we can write:
\[ AB^2 = AC^2 + CB^2 \]
- Here, we know:
- AB = 40 m (the distance from the base to where the top touches the ground)
- AC = 9 m (the height from the ground to the break point)
- CB is the length of the broken part of the tree, which we need to find.

5. **Calculate CB**:
- First, we need to find the length of CB using the Pythagorean theorem:
\[ 40^2 = 9^2 + CB^2 \]
\[ 1600 = 81 + CB^2 \]
\[ CB^2 = 1600 - 81 = 1519 \]
\[ CB = \sqrt{1519} \approx 39.0 \text{ m} \]

6. **Find the Total Height of the Tree**:
- The total height of the tree before it was broken (AD) is the sum of the height at which it broke (AC) and the length of the broken part (CB):
\[ AD = AC + CB \]
\[ AD = 9 + 39.0 \approx 48.0 \text{ m} \]

7. **Conclusion**:
- Therefore, the height of the tree before it was broken is approximately **48.0 meters**.