In a right-angled triangle, the angle between the hypotenuse and the median drawn

In a right-angled triangle, the angle between the hypotenuse and the median drawn to it is 76. Find the larger of the two acute angles of the triangle.

1. Let us introduce the designation of the vertices of the triangle by the symbols A, B, C. Angle C = 90 °. CK is the median.

AK = ВK. Angle AKC = 76 °.

2. According to the properties of a right-angled triangle, CK = AB / 2.

3. AB = AK + ВK. Therefore, CK = AK. The ACK triangle is isosceles. The angles at its base are equal. That is, the angle CАК = АСК.

4. We calculate their value:

5. Angle angle CAK = angle ACK = (180 ° – 76 °) / 2 = 52 °.

6. Angle B = 180 ° – 52 ° – 90 ° = 38 °.

Answer: the large acute angle of triangle ABC is angle A, equal to 52 °.