1. **State the problem:** Barbara has a wooden cabin 42 meters wide. She uses 27-meter beams for the roof, which meet at the middle of the cabin's width. We need to find the angle of elevation of the roof beams. 2. **Understand the setup:** The beams form two equal sides of a triangle with the base 42 meters. The beams meet at the peak, and a perpendicular line from the peak to the base bisects the base into two segments of 21 meters each. 3. **Identify the triangle:** We have a right triangle formed by half the base (21 m), the beam (27 m), and the vertical height (unknown). The angle of elevation $\theta$ is between the beam and the horizontal base. 4. **Use the cosine formula for the angle:** $$\cos(\theta) = \frac{\text{adjacent side}}{\text{hypotenuse}} = \frac{21}{27}$$ 5. **Calculate the angle:** $$\theta = \cos^{-1}\left(\frac{21}{27}\right) = \cos^{-1}\left(\frac{7}{9}\right)$$ 6. **Evaluate the inverse cosine:** Using a calculator, $$\theta \approx 38.94^\circ$$ 7. **Round the answer:** Rounded to the nearest tenth, $$\theta \approx 38.9^\circ$$ **Final answer:** The angle of elevation of the roof beams is approximately **38.9 degrees**.