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The problem in the image describes a tree that has broken due to a storm. Here is the summary of the problem:

- The broken part of the tree touches the ground.
- The distance between the base of the tree (its root) and the point where the broken part touches the ground is **8 meters**.
- The broken part makes an angle of **60°** with the ground.
  
We are asked to find the total height of the tree.

### Solution:
This problem can be solved using trigonometry. The scenario describes a right triangle formed by:

- The vertical part of the tree that remains upright (let's call it \( h_1 \)).
- The broken part of the tree (let's call its length \( h_2 \)).
- The distance on the ground between the tree base and the point where the tree touches the ground is given as 8 m.

The broken part forms a hypotenuse in this right triangle, where:
- The adjacent side (along the ground) is 8 m.
- The angle formed with the ground is \( 60^\circ \).

Using the cosine function:
\[
\cos(60^\circ) = \frac{\text{Adjacent (ground distance)}}{\text{Hypotenuse (broken tree part)}}
\]
\[
\cos(60^\circ) = \frac{8}{h_2}
\]

Since \( \cos(60^\circ) = 0.5 \), we can solve for \( h_2 \):
\[
0.5 = \frac{8}{h_2}
\]
\[
h_2 = 16 \text{ meters}
\]

Now that we know the length of the broken part of the tree (\( h_2 = 16 \) m), we can find the height of the upright part of the tree using the sine function:
\[
\sin(60^\circ) = \frac{\text{Opposite (upright height)}}{\text{Hypotenuse (broken part)}}
\]
\[
\sin(60^\circ) = \frac{h_1}{16}
\]
Since \( \sin(60^\circ) = \frac{\sqrt{3}}{2} \), we get:
\[
\frac{\sqrt{3}}{2} = \frac{h_1}{16}
\]
\[
h_1 = 16 \times \frac{\sqrt{3}}{2} = 8\sqrt{3} \approx 13.86 \text{ meters}
\]

Finally, the total height of the tree is the sum of \( h_1 \) (the upright part) and \( h_2 \) (the broken part):
\[
\text{Total height} = h_1 + h_2 = 13.86 + 16 = 29.86 \text{ meters}
\]

### Conclusion:
The total height of the tree is approximately **29.86 meters**.

---

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. How would the total height change if the broken part made a 45° angle with the ground?
2. How does the use of trigonometry help in solving real-world problems like this?
3. What would be the total height if the ground distance was 10 meters?
4. How can the Pythagorean theorem be applied in problems involving right triangles?
5. What is the relationship between the angle and the length of the broken part of the tree?

**Tip:** Always sketch a diagram when solving geometry or trigonometry problems to help visualize the relationships between angles and sides.

A tree was broken due to a heavy storm. The broken part of the tree touches the ground, and the distance between the base of the tree and the point where the broken part touches the ground is 8 meters. The broken part makes a 60° angle with the ground. Find the total height of the tree.

Solve a real-world problem using trigonometry to find the total height of a tree. The tree's broken part forms a 60° angle with the ground, and the distance between the base and the broken part is 8 meters. Learn step-by-step how to use trigonometric ratios to calculate the tree's full height.

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