Inside the square, the side of which is 1 cm, a point F is marked such that the angle
| May 8, 2021 | education
Inside the square, the side of which is 1 cm, a point F is marked such that the angle AFB is 75 degrees, and the angle FAD = 60 degrees. Find the leg length AF.
Since ABCD is a square, all of its interior angles are straight.
Determine the value of the angle BAF.
Angle BAF = BAD – FAD = 90 – 60 = 30.
In triangle ABF, define the value of the angle ABF.
Angle ABF = (180 – BAF – AFB) = (180 – 30 – 75) = 75.
Then triangle ABF is isosceles with base BF, and therefore AF = AB = 1 cm.
Answer: The length of the AF segment is 1 cm.
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