In triangle ABC it is known that ∠ACB = 90 °, ∠A = ∠B = 45 °, CK-height. Find side AB if CK = 7 cm.

1. Triangle ABC is isosceles, since the angles on the side AB (adjacent to it) are equal.
2. In a given triangle, the height of the SC also performs the functions of the median, that is, it divides the side AB to which it is drawn into two identical segments AK and ВK.
3. We calculate the degree value ∠ACK of the ACK triangle:
∠АСК = 180 ° – 45 ° – 90 ° = 45 °. The ACK triangle is also isosceles, since the angles at its base are equal. Therefore, AK = СK = 7 cm.
4. We calculate the length of the side AB:
AB = 7 + 7 = 14 cm.
Answer: AB length is 14 cm.