1. **Stating the problem:** We have a right triangle HJT with angles 60°, 30°, and 90° at T. The sides are labeled as follows: HJ = 2x (hypotenuse), HT = x (shorter leg), and TJ = x\sqrt{3} (longer leg). We need to find the length of the longer leg TJ. 2. **Formula and rules:** In a 30°-60°-90° triangle, the sides have a fixed ratio: the hypotenuse is twice the shorter leg, and the longer leg is the shorter leg times \sqrt{3}. 3. **Given:** Hypotenuse HJ = 2x, shorter leg HT = x, longer leg TJ = x\sqrt{3}. 4. **Finding the longer leg:** Since the longer leg TJ = x\sqrt{3}, and the hypotenuse is 2x, the length of the longer leg is directly given by the formula. 5. **Final answer:** The length of the longer leg TJ is $$x\sqrt{3}$$ inches.