Final answer:
The area of the right triangle with a hypotenuse of 26 inches and one leg of 10 inches is calculated to be 120 square inches.
Step-by-step explanation:
To find the area of the right triangle, we need the lengths of both legs. We have one leg that is 10 inches and a hypotenuse of 26 inches. Using the Pythagorean theorem (a² + b² = c²), we can find the other leg. Here, c = 26 inches, and a or b is 10 inches. We are looking for the other leg (let's call it b).
10² + b² = 26²
100 + b² = 676
b² = 676 - 100
b² = 576
b = √576
b = 24 inches
Now, to find the area of the triangle, use the formula 1/2 * base * height, which in the case of a right triangle is 1/2 * one leg * other leg.
Area = 1/2 * 10 inches * 24 inches
Area = 120 square inches
Thus, the area of the right triangle is 120 square inches.