1. **State the problem:** We need to find the height $h$ of the tower. The triangle is right-angled with a horizontal side of 125 m, a vertical side of 1.8 m (man's height), and an angle of 45° between the ground and the hypotenuse. 2. **Identify the triangle parts:** The hypotenuse runs from the man's eye level to the top of the tower. The vertical height $h$ is from the ground to the top of the tower, so it includes the man's height plus the vertical leg of the triangle formed by the hypotenuse and the ground. 3. **Use trigonometry:** The angle between the ground and the hypotenuse is 45°, and the adjacent side (ground) is 125 m. We can find the opposite side (vertical leg above the man's height) using the tangent function: $$\tan(45^\circ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{x}{125}$$ Since $\tan(45^\circ) = 1$, we have: $$1 = \frac{x}{125}$$ 4. **Solve for $x$:** $$x = 125$$ 5. **Calculate total height $h$:** $$h = \text{man's height} + x = 1.8 + 125 = 126.8$$ 6. **Final answer:** $$h = 126.8$$ meters. This means the tower is 126.8 meters tall from the ground to the top.