1. **Problem 15: Find the missing side of a right triangle with sides 12 ft (hypotenuse), 6 ft, and 7.1 ft.** 2. Use the Pythagorean theorem for right triangles: $$a^2 + b^2 = c^2$$ where $c$ is the hypotenuse. 3. Check if the given sides satisfy the theorem: $$6^2 + 7.1^2 = 36 + 50.41 = 86.41$$ and $$12^2 = 144$$. Since $86.41 \neq 144$, the sides do not form a right triangle as given. 4. Since the hypotenuse is 12 ft, and one leg is 6 ft, find the other leg $b$ using $$b = \sqrt{12^2 - 6^2} = \sqrt{144 - 36} = \sqrt{108} = 10.39$$ ft (rounded to two decimals). 5. The given 7.1 ft does not fit the right triangle with hypotenuse 12 ft and leg 6 ft; the missing measurement is approximately 10.39 ft. 6. **Problem 17: Find the missing height of a parallelogram with base 4.6 cm, one height 4 cm, and missing height ? cm.** 7. The area of a parallelogram is $$\text{Area} = \text{base} \times \text{height}$$. 8. Assuming the parallelogram has two different heights corresponding to two different bases, and the area is constant, use the relation $$\text{base}_1 \times \text{height}_1 = \text{base}_2 \times \text{height}_2$$. 9. Given $$4.6 \times ? = 4 \times 4$$, solve for the missing height: $$? = \frac{4 \times 4}{4.6} = \frac{16}{4.6} = 3.48$$ cm (rounded to two decimals). **Final answers:** - Missing side of the right triangle: approximately $10.39$ ft. - Missing height of the parallelogram: approximately $3.48$ cm.