Inside the square, the side of which is 1 cm, is marked with a point,

Inside the square, the side of which is 1 cm, is marked with a point, F, such that the angle AFB is 75 degrees, and the angle. FAD = 60 degrees. Find the leg length AF.

Since ABCD is a square, its angles are 90.

Angle BAF = BAD – FAD = 90 – 60 = 30.

Then in the triangle ABF the angle ABF = (180 – AFB – BAF) = (180 – 75 – 30) = 75.

Since in triangle BAF the angles at the base of BF are equal, then triangle BAF is isosceles, and therefore AF = AB = 1 cm.

Answer: The length of the AF side is 1 cm.