1. **State the problem:** Find the angle of elevation $x$ of the sun when a tree 10 yards tall casts a shadow 14 yards long. 2. **Identify the triangle sides:** The tree height is the side opposite the angle $x$, so opposite side $=10$ yards. The shadow length is the adjacent side to angle $x$, so adjacent side $=14$ yards. 3. **Formula used:** The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side: $$\tan(x) = \frac{\text{opposite}}{\text{adjacent}}$$ 4. **Apply the formula:** $$\tan(x) = \frac{10}{14}$$ 5. **Calculate the angle:** $$x = \tan^{-1}\left(\frac{10}{14}\right)$$ 6. **Evaluate the inverse tangent:** $$x = \tan^{-1}(0.7143)$$ Using a calculator, $$x \approx 35.54^\circ$$ 7. **Round to the nearest degree:** $$x \approx 36^\circ$$ **Final answer:** The angle of elevation of the sun is approximately $36^\circ$.