1. **State the problem:** A construction worker 6.5 feet tall stands 8 feet away from a two-storey building 40 feet high. We need to find the angle of elevation from the worker's eyes to the top of the building, correct to 1 decimal place. 2. **Identify the relevant quantities:** - Height of building: 40 feet - Height of worker: 6.5 feet - Distance from worker to building: 8 feet 3. **Calculate the vertical height difference:** The angle of elevation is measured from the worker's eye level, so the vertical height difference is: $$40 - 6.5 = 33.5$$ feet 4. **Use the tangent function:** The angle of elevation $\theta$ satisfies: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{33.5}{8}$$ 5. **Calculate the angle:** $$\theta = \tan^{-1}\left(\frac{33.5}{8}\right)$$ 6. **Evaluate the arctangent:** $$\theta = \tan^{-1}(4.1875)$$ Using a calculator, $$\theta \approx 76.5^\circ$$ **Final answer:** The angle of elevation to the top of the building is approximately **76.5 degrees**.