In a right-angled triangle, one of the legs is 31, and the angle opposite it is 45. Find the area of the triangle.

In a right-angled triangle, one of the angles is 90 degrees, the second is 45 degrees by condition, so the third angle is 180-90-45 = 45 degrees. We get a right-angled triangle with two equal acute angles, each of which is equal to 45 degrees. If two angles in a triangle are equal, then it is isosceles, therefore we have a right-angled isosceles triangle with legs equal to 31. Its area is equal to half of the product of legs: S = 0.5 * 31 * 31 = 480.5.