Find the area of a right-angled triangle if its leg and hypotenuse are 28 and 100, respectively.

The area of a right-angled triangle is half the product of its legs. S = 1/2 * ab.

We find the unknown leg of a right-angled triangle by the Pythagorean theorem: In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the legs. c² = a² + b², where a and b are the legs of the triangle, c is the hypotenuse of the triangle.

a² = c² – b²;

a² = 100² – 28² = 10000 – 784 = 9216;

a = √9216 = 96.

S = 1/2 * 96 * 28 = 2688/2 = 1344.

Answer. 1344.