1. **State the problem:** We need to find the height $h$ of the tower given a right triangle where the angle between the hypotenuse and the horizontal base is $45^\circ$, the horizontal distance is 125 m, and the man's height is 1.8 m. 2. **Identify the known values:** - Angle $\theta = 45^\circ$ - Horizontal distance (adjacent side) $= 125$ m - Man's height $= 1.8$ m 3. **Use the tangent function:** The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ Here, the opposite side is the height difference between the tower and the man, i.e., $h - 1.8$. 4. **Set up the equation:** $$\tan(45^\circ) = \frac{h - 1.8}{125}$$ Since $\tan(45^\circ) = 1$, the equation simplifies to: $$1 = \frac{h - 1.8}{125}$$ 5. **Solve for $h$:** Multiply both sides by 125: $$125 = h - 1.8$$ Add 1.8 to both sides: $$h = 125 + 1.8 = 126.8$$ **Final answer:** $$h = 126.8 \text{ meters}$$