Triangle ABC, angle C = 90 degrees, angle A = 45 degrees, AC = 2√2 Find AB?

If angle A = 45 degrees, then angle B is also 45 degrees.

This means that the legs are also equal, that is, BC = AC = 2.

Following the Pythagorean theorem (the square of the hypotenuse is equal to the sum of the squares of the legs), we find the hypotenuse AB.

AB˄2 = (2) ˄2 + (2) ˄2;

AB˄2 = 8 +8;

AB˄2 = 16;

AB = 4 cm.

Answer: 4 cm.