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

In a right-angled triangle, the angle between the hypotenuse and the median drawn to the hypotenuse is 25 degrees. Find the smallest angle 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 = BK. Angle AKC = 25 °.

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

3. AB = AK + BK. Therefore, CK = AK. The ACK triangle is isosceles. The angles at its base are equal. Angle ACK = angle ACK.

4. We calculate their value:

5. Angle CАК = angle АСК = (180 ° – 25 °) / 2 = 155: 2 = 77.5 °.

6. Angle B = 180 ° – 77.5 ° – 90 ° = 12.5 °.

Answer: the smaller acute angle of triangle ABC is angle B, equal to 12.5 °.