1. **State the problem:** A bird sits on top of a lamppost. The angle of depression from the bird to the feet of an observer is 35°. The distance from the bird to the observer is 25 meters. We need to find the height of the lamppost. 2. **Understand the scenario:** The angle of depression is the angle between the horizontal line from the bird and the line of sight to the observer's feet. This forms a right triangle where: - The hypotenuse is 25 meters (distance from bird to observer). - The angle at the bird is 35°. - The vertical leg is the height of the lamppost (which we want to find). 3. **Use trigonometry:** In the right triangle, the height corresponds to the side opposite the angle of depression. The hypotenuse is the distance from the bird to the observer. The sine function relates opposite side and hypotenuse: $$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$$ 4. **Apply the formula:** $$\sin(35^\circ) = \frac{\text{height}}{25}$$ 5. **Solve for height:** $$\text{height} = 25 \times \sin(35^\circ)$$ 6. **Calculate the value:** $$\sin(35^\circ) \approx 0.574$$ So, $$\text{height} = 25 \times 0.574 = 14.35$$ meters **Final answer:** The lamppost is approximately **14.35 meters** tall.