The median CK is drawn in the right-angled triangle ABC (c = 90), the AKC angle is 42. Find the angle A

1. It is known that

a) in a right-angled triangle, the median drawn from the vertex of the right angle is equal to half the hypotenuse,

b) in an isosceles triangle, the angles at the base are equal.

2. By the condition of the problem, KC is the median, hence aK = 1/2 ab, and by the property of the median drawn from a right angle, CK = 1/2 ab, hence aK = CK.

Formed triangle aCK is isosceles, and angle A = angle aKC.

According to the condition of the problem, the angle aKC is 42 *, which means that the angle A = 42 *.

Answer: Angle A is 42 *.