In a right-angled triangle, one of the legs is 7, and the acute angle adjacent to it is 45 degrees.

In a right-angled triangle, one of the legs is 7, and the acute angle adjacent to it is 45 degrees. Find the area of the triangle.

Let ABC be a right-angled triangle, angle C = 90 degrees, AC = 7 and BC — legs, AB — hypotenuse, angle A = 45 degrees.
Find the degree measure of the angle B:
angle A + angle B + angle C = 180 degrees (according to the theorem on the sum of the angles of a triangle);
45 + angle B + 90 = 180;
angle B = 180 – 135;
angle B = 45 degrees.
Since angle B = 45 degrees and angle A = 45 degrees, therefore angle A = angle B. Therefore, triangle ABC is a right-angled isosceles triangle with sides AC and BC, base AB and angles at base A and B.
The area of ​​a right-angled triangle is equal to half the product of its legs:
S = AC * BC / 2;
S = 7 * 7/2 = 49/2 = 24.5 (conventional units).
Answer: S = 24.5 conventional units.