1. **Stating the problem:** Given an angle $\alpha = 25^\circ$ and a distance $s = 45$ m, we want to find the height or vertical component related to these values. 2. **Formula used:** To find the vertical height $h$ from the angle and distance, we use the sine function from trigonometry: $$h = s \times \sin(\alpha)$$ 3. **Explanation:** The sine of an angle in a right triangle is the ratio of the opposite side (height) to the hypotenuse (distance $s$). Multiplying $s$ by $\sin(\alpha)$ gives the vertical height. 4. **Calculation:** $$h = 45 \times \sin(25^\circ)$$ Using a calculator or sine table: $$\sin(25^\circ) \approx 0.4226$$ So, $$h = 45 \times 0.4226 = 19.017$$ 5. **Final answer:** The vertical height corresponding to the angle and distance is approximately $$h \approx 19.02 \text{ meters}$$ This height can be interpreted as the vertical component of the distance $s$ at angle $\alpha$.