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This problem involves a tilted pole casting a shadow, where we need to find the length of the pole. Let's break it down using trigonometry.

### Given Information:
- The angle of elevation of the sun is \(49^\circ\).
- The pole leans at an angle of \(8^\circ\) from the vertical.
- The shadow on the ground is \(45\) feet long.

### Approach:
1. **Identify the angle of the pole with the horizontal ground:**
   Since the pole is tilted \(8^\circ\) from the vertical, the angle between the pole and the horizontal ground is:
   \[
   90^\circ - 8^\circ = 82^\circ
   \]

2. **Set up a right triangle:**
   Let:
   - \(AB = 45\) feet (the shadow length).
   - \(AC\) be the length of the pole (which we want to find).
   - Angle \(A\) (between \(AB\) and \(AC\)) is \(49^\circ\).

3. **Use the Law of Sines**:
   \[
   \frac{AC}{\sin(49^\circ)} = \frac{45}{\sin(82^\circ)}
   \]
   Solving for \(AC\):
   \[
   AC = \frac{45 \cdot \sin(49^\circ)}{\sin(82^\circ)}
   \]

4. **Calculate the value:**
   Plugging in the values:
   - \(\sin(49^\circ) \approx 0.755\)
   - \(\sin(82^\circ) \approx 0.990\)

   \[
   AC \approx \frac{45 \cdot 0.755}{0.990} \approx \frac{33.975}{0.990} \approx 34.3 \text{ feet}
   \]

### Final Answer:
The length of the pole is approximately **34 feet**, rounded to the nearest foot.

Would you like further clarification or additional details?

### Related Questions:
1. How would the pole’s length change if it leaned at a different angle from the vertical?
2. What would be the pole’s shadow length if the sun's elevation changed to \(60^\circ\)?
3. How can we find the height of the pole if the leaning angle and shadow are known?
4. What if the ground was not level? How would that affect the calculation?
5. How can trigonometry help solve real-world problems involving angles and distances?

**Tip:** In right-triangle problems, always verify whether to use sine, cosine, or tangent based on the given angles and sides.

A pole leans away from the sun at an angle of 8° to the vertical. When the elevation of the sun is 49°, the pole casts a shadow 45 ft long on level ground. How long is the pole?

Learn how to find the length of a pole leaning at an angle, given the elevation of the sun and shadow length. This problem uses trigonometric concepts, including the Law of Sines, to calculate the pole length. Suitable for high school students studying trigonometry.

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