Angle C = 90 degrees, Angle A = 60 degrees, AB + AC = 1.8 AB-?

We calculate the degree measure of the angle B = 180 – A – C = 180 – 60 – 90 = 30.

According to the theorem, in a right-angled triangle, the side opposite to an angle of 30 degrees is equal to half the hypotenuse. That is, AC = 0.5 * AB.

According to the condition AB + AC = 1.8, we substitute the found expression AC = 0.5 * AB into the equation and solve it:

AB + 0.5 * AB = 1.8;

1.5 * AB = 1.8;

AB = 1.8 / 1.5;

AB = 1.2.

Answer: AB = 1.2.