1. **Problem statement:** Shawn measures the angle of elevation to the top of a 450 feet high tower as 32°. We need to find the horizontal distance from Shawn to the base of the tower. 2. **Diagram and triangle setup:** - Right triangle with: - Opposite side (height of tower) = 450 feet - Angle of elevation = 32° - Adjacent side (distance from Shawn to tower base) = unknown, call it $x$ 3. **Formula used:** 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, $\theta = 32^\circ$, opposite = 450, adjacent = $x$. 4. **Set up the equation:** $$\tan(32^\circ) = \frac{450}{x}$$ 5. **Solve for $x$:** $$x = \frac{450}{\tan(32^\circ)}$$ 6. **Calculate $\tan(32^\circ)$:** Using a calculator, $\tan(32^\circ) \approx 0.6249$ 7. **Find $x$:** $$x = \frac{450}{0.6249} \approx 720.1$$ 8. **Answer:** Shawn is approximately 720.1 feet away from the base of the tower. This means the horizontal distance from Shawn to the tower base is about 720 feet.