The image presents a problem where you are asked to calculate the height of a tree based on the given angles and distances in the diagram. Here's the setup from the image:

1. The distance from the observer to the tree's base is 20 meters.
2. There are two angles of elevation involved:
   • The lower angle is $22.5^\circ$.
   • The upper angle is $43^\circ$.
3. The observer is standing 1.6 meters above the ground.

To solve for the height of the tree, we can use trigonometric functions based on the right triangles formed by the observer’s line of sight.

Step-by-step solution:

1. Height between the ground and the 43° angle of elevation: $h_1 = 20 \times \tan(43^\circ)$

2. Height between the ground and the 22.5° angle of elevation: $h_2 = 20 \times \tan(22.5^\circ)$

3. The total height of the tree can be found by subtracting the difference in heights calculated by the angles and adding the observer's eye level (1.6 meters): $\text{Tree Height} = (h_1 - h_2) + 1.6$

Let me calculate that.The total height of the tree is approximately 11.97 meters.

Would you like more details on the calculations or have any questions?

Here are some follow-up questions:

1. What is the significance of using trigonometry in height calculations?
2. How does the observer's height affect the total height of the tree?
3. Could we calculate the height using a different trigonometric function?
4. How would the height change if the distance to the tree was increased?
5. Can you think of another method to measure inaccessible heights?

Tip: Understanding how to apply trigonometry to real-world problems can significantly improve your problem-solving skills.