The upper part of a tree broken over by the wind makes an angle of `60^(@)` with the ground and the horizontal distance from the foot of the tree to the point where the top of the tree meets the ground is 10 metres. Find the height of the tree before broken.

Answer

To find the height of the tree before it was broken, we can break the problem down into steps using trigonometric principles.

### Step-by-Step Solution:

1. **Understanding the Problem:**
- The upper part of the tree makes an angle of \(60^\circ\) with the ground.
- The horizontal distance from the foot of the tree to the point where the top of the tree meets the ground is 10 meters.

2. **Identify the Components:**
- Let \(h\) be the height of the part of the tree that is still standing.
- Let \(x\) be the length of the broken part of the tree (the hypotenuse of the triangle formed).

3. **Using Tangent to Find \(h\):**
- We can use the tangent function, which relates the opposite side (height of the standing part of the tree) to the adjacent side (horizontal distance).
- The formula is:
\[ \tan(60^\circ) = \frac{h}{10} \]
- We know that \(\tan(60^\circ) = \sqrt{3}\).
- Therefore, we can write:
\[ \sqrt{3} = \frac{h}{10} \]
- Rearranging gives:
\[ h = 10\sqrt{3} \]

4. **Calculating \(h\):**
- Now, we calculate \(h\):
\[ h = 10\sqrt{3} \approx 10 \times 1.732 = 17.32 \text{ meters} \]

5. **Using Cosine to Find \(x\):**
- Next, we use the cosine function to find the length of the broken part of the tree.
- The formula is:
\[ \cos(60^\circ) = \frac{10}{x} \]
- We know that \(\cos(60^\circ) = \frac{1}{2}\).
- Therefore, we can write:
\[ \frac{1}{2} = \frac{10}{x} \]
- Rearranging gives:
\[ x = 20 \text{ meters} \]

6. **Finding the Total Height of the Tree:**
- The total height of the tree before it was broken is the sum of the standing part and the broken part:
\[ \text{Total Height} = h + x = 17.32 + 20 = 37.32 \text{ meters} \]

### Final Answer:
The height of the tree before it was broken is approximately **37.32 meters**.