In the triangle ABC, the median CK = 15√2 is drawn and the component with the AC side

In the triangle ABC, the median CK = 15√2 is drawn and the component with the AC side is an angle of 30 degrees. Find AB if angle A is 45 degrees.

Let’s build the height of the KH to the AC side of the ABC triangle.

In a right-angled triangle ACK, the leg KH lies opposite an angle of 30, then KH = CK / 2 = 15 * √2 / 2 cm.

The triangle AHK is rectangular and isosceles, since the angle is A = 45, then AK = KH * Sin45 = 15 * √2 / 2 * √2 / 2 = 15 cm.

Since CК is the median of the triangle, then AB = 2 * AK = 2 * 15 = 30 cm.

Answer: The length of the AB side is 30 cm.