Final answer:
To find the length of the missing leg in a right triangle, we use the Pythagorean theorem. For the second question, to find the length of the hypotenuse, we again use the Pythagorean theorem.
Step-by-step explanation:
To find the length of the missing leg in a right triangle, we can use the Pythagorean theorem, which states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, one leg is 9 units and the hypotenuse is 15 units. Let's call the missing leg x. The equation becomes 9^2 + x^2 = 15^2. Solving for x, we get x = sqrt(225 - 81) = sqrt(144) = 12. Therefore, the length of the missing leg is 12 units.
For the second question, given the lengths of the two legs of a right triangle as 10 inches and 12 inches, we can find the length of the hypotenuse using the Pythagorean theorem again. Let's call the length of the hypotenuse c. The equation is 10^2 + 12^2 = c^2. Simplifying, we get 100 + 144 = c^2. Adding, we get 244 = c^2. Therefore, the length of the hypotenuse is sqrt(244), which is approximately 15.62 inches.