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The problem presented in the image describes an ecologist trying to find the height of a redwood tree across a creek. Here's a breakdown of the problem:

- From point \( A \), the angle of elevation to the top of the tree is \( 8.8^\circ \).
- The ecologist walks 24.8 feet at a right angle from point \( A \) to point \( B \).
- From point \( B \), the angle between the line \( AB \) and a line extending from \( B \) to the top of the tree is \( 86.1^\circ \).
  
We are tasked with finding the height \( h \) of the tree, rounding the answer to one decimal place.

### Approach:

We will use trigonometric functions to solve this problem. The process involves using both the given angles and distances to set up a system of equations. Let me solve it step by step.The height of the tree is approximately \( 3.8 \) feet, rounded to one decimal place.

Would you like more details or have any questions?

Here are 5 related questions to consider:
1. How does the tangent function relate to right-angled triangles?
2. What other methods could be used to solve this problem if more angles were given?
3. Can you calculate the horizontal distance from point A to the base of the tree?
4. How would the problem change if the angle of elevation from point A were larger?
5. What is the significance of the right-angle distance walked between points A and B?

**Tip:** Understanding trigonometric relationships is key in solving height and distance problems, especially in navigation or surveying tasks.

An ecologist wishes to find the height of a redwood tree that is on the other side of a creek. From point A, he finds that the angle of elevation to the top of the tree is 8.8°. He then walks 24.8 feet at a right angle, from point A to point B. There he finds that the angle between AB and a line extending from B to the tree is 86.1°. What is the height h of the tree? (Round your answer to one decimal place).

An ecologist measures the height of a redwood tree across a creek using trigonometry. By walking 24.8 feet from point A to B and measuring angles of 8.8° and 86.1°, learn how to calculate the tree's height step by step. Suitable for high school students.

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