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The problem in the image reads:

"A tree was broken due to the heavy storm. The broken part of the tree touches the ground, and the distance between the bottom of the tree and its root is 8m. The tree makes an angle of 60° with the ground. Find the total height of the tree."

This is a typical trigonometry problem where the tree forms a right triangle with the ground, and we need to find the total height.

### Solution:

Let:
- \( h_1 \) be the height of the standing part of the tree.
- \( h_2 \) be the length of the broken part of the tree that touches the ground.

We know:
- The distance between the base of the tree and where the broken part touches the ground (the horizontal distance) is 8 meters. 
- The broken part makes a \( 60^\circ \) angle with the ground.

Using trigonometry, specifically the cosine function, we can relate the length of the broken part of the tree to the horizontal distance:

\[
\cos(60^\circ) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{8}{h_2}
\]

Since \( \cos(60^\circ) = \frac{1}{2} \), we get:

\[
\frac{1}{2} = \frac{8}{h_2}
\]

Solving for \( h_2 \):

\[
h_2 = 16 \, \text{m}
\]

Now that we know the broken part of the tree has a length of 16 meters, we also need to find the height of the standing part of the tree, \( h_1 \). From trigonometry, we use the sine function:

\[
\sin(60^\circ) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{h_1}{h_2}
\]

Since \( \sin(60^\circ) = \frac{\sqrt{3}}{2} \), we get:

\[
\frac{\sqrt{3}}{2} = \frac{h_1}{16}
\]

Solving for \( h_1 \):

\[
h_1 = 16 \times \frac{\sqrt{3}}{2} = 8\sqrt{3} \, \text{m}
\]

Approximating \( \sqrt{3} \approx 1.732 \):

\[
h_1 \approx 8 \times 1.732 = 13.856 \, \text{m}
\]

Thus, the total height of the tree is:

\[
\text{Total height} = h_1 + h_2 = 13.856 + 16 \approx 29.856 \, \text{m}
\]

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

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Would you like further details, or do you have any questions?

Here are 5 related questions to deepen understanding:
1. How would the answer change if the angle was 45° instead of 60°?
2. What is the significance of using trigonometric functions in real-world problems?
3. Can you calculate the height using tangent instead of sine and cosine?
4. What would happen if the horizontal distance was increased?
5. How could we solve this problem graphically?

**Tip**: Always check if the triangle formed by the tree and the ground is a right triangle when applying trigonometric ratios.

A tree was broken due to the heavy storm. The broken part of the tree touches the ground, and the distance between the bottom of the tree and its root is 8m. The tree makes an angle of 60° with the ground. Find the total height of the tree.

Discover how to calculate the total height of a tree that was broken in a storm using trigonometric ratios. This problem involves determining the height of a tree that forms a right triangle with the ground and includes key formulas like sine and cosine. Perfect for students in Grades 9-11.

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