1. **State the problem:** A girl 1.2m tall is standing 25m away from a tower 18m high. We need to find the angle of elevation from her eyes to the top of the tower. 2. **Identify the relevant triangle and sides:** The vertical height difference between the top of the tower and the girl's eyes is $$18 - 1.2 = 16.8$$ meters. The horizontal distance from the girl to the tower is 25 meters. 3. **Formula used:** The angle of elevation $$\theta$$ can be found using the tangent function in a right triangle: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ where the opposite side is the height difference (16.8m) and the adjacent side is the horizontal distance (25m). 4. **Calculate the tangent:** $$\tan(\theta) = \frac{16.8}{25}$$ 5. **Find the angle $$\theta$$:** Use the inverse tangent (arctan) function: $$\theta = \tan^{-1}\left(\frac{16.8}{25}\right)$$ 6. **Evaluate the angle:** $$\theta = \tan^{-1}(0.672) \approx 34^\circ$$ **Final answer:** The angle of elevation of the top of the tower from the girl's eyes is approximately **34 degrees**.