1. **Stating the problem:** We have a right triangle where the vertical side is 6 units, and the horizontal side is given as 10 feet 8 inches. The angle adjacent to the horizontal side is 17°40'. 2. **Convert measurements:** Convert 10 feet 8 inches into a single unit (feet). Since 8 inches = \(\frac{8}{12} = 0.6667\) feet, the total horizontal length is \(10 + 0.6667 = 10.6667\) feet. 3. **Calculate the hypotenuse:** Use the Pythagorean theorem to find the hypotenuse \(c\): $$ c = \sqrt{6^2 + 10.6667^2} = \sqrt{36 + 113.778} = \sqrt{149.778} \approx 12.24 $$ 4. **Verify the given angle:** Use tangent, since \(\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}\). Compute \(\tan(17°40')\). Convert to decimal degrees: $$ 17°40' = 17 + \frac{40}{60} = 17.6667° $$ Calculate \(\tan(17.6667°) \approx 0.3191\). Calculate \(\frac{6}{10.6667} \approx 0.5625\), which is different from 0.3191. So the given sides and angle do not fit a right triangle; the angle appears inconsistent with the side lengths. 5. **Summary:** Given the vertical side 6 and horizontal side 10'8'' (10.6667 feet), the angle adjacent to the horizontal side should be: $$ \theta = \arctan\left(\frac{6}{10.6667}\right) = \arctan(0.5625) \approx 29.4° $$ The angle 17°40' is likely a mislabel or corresponds to a different side. **Final answer:** Converted horizontal side is 10.6667 feet and hypotenuse is approximately 12.24 feet. The angle adjacent to the horizontal side with these lengths is approximately 29.4°, not 17°40'.