In a right-angled triangle, one of the legs is 10, and the angle opposite it is 45 degrees. Find the area of the triangle.

1. Let us introduce the designation of the vertices of the triangle by the symbols A, B, C. Angle C = 90 °. BC = 10 units. Angle BAC = 45 °.

2. We calculate the value of the angle ABC, based on the fact that the total value of the inner angles of the triangle is 180 °:

Angle ABC = 180 ° – 45 ° – 90 ° = 45 °.

3. Angles BAC and ABC at the base AB of triangle ABC are equal. Therefore, this triangle is isosceles. Hence, AC = BC = 10 units.

4. The area of the triangle ABC = AC x BC: 2 = 10 x 10: 2 = 50 units ^ 2.