1. We are given a vertical pole casting a shadow of 1.8 meters when the sun's elevation angle is 63.5 degrees. We need to find the height of the pole. 2. The problem can be solved using trigonometry. Let $h$ be the height of the pole. 3. The sun’s elevation angle of 63.5 degrees corresponds to the angle between the ground and the line from the top of the pole to the tip of the shadow. 4. We use the tangent function which relates the opposite side (height $h$) to the adjacent side (shadow length 1.8 m): $$\tan(63.5^\circ) = \frac{h}{1.8}$$ 5. Solve for $h$: $$h = 1.8 \times \tan(63.5^\circ)$$ 6. Calculate $\tan(63.5^\circ)$ using a calculator: $$\tan(63.5^\circ) \approx 2.007$$ 7. Multiply to find $h$: $$h = 1.8 \times 2.007 = 3.6126$$ 8. Round to 1 decimal place: $$h \approx 3.6$$ meters **Final answer:** The height of the pole is approximately 3.6 meters.