In a right triangle, one of the legs is 24, and the acute angle adjacent to it is 45 °. Find the area of the triangle.

By the theorem on the sum of the angles of a triangle, the third angle can be calculated, it is equal to 180 ° -90 ° -45 ° = 45 °.
Therefore, this triangle is isosceles (by the first property).
Those. the legs of this triangle are equal.
The area of a right triangle = ab / 2, where a and b are legs. Then:
S triangle = 24 * 24/2 = 288
Answer: S triangle = 288