How to calculate the formula for calculation?

Question

Mathematics

Hello.
Help me calculate the formula for calculating the length of the arc A->B (see screenshot), knowing the height from the bottom of the steep.

Answer 1

L = π * R * acos((R - P) / R)
where:
L - desired length of the arc
R - radius of the circle, equal to half the diameter, which is equal to the side of the circumscribing square
P - height from the bottom point of the circle
for the numbers indicated in the figure:
P = 25 cm
R = 100 cm / 2 = 50 cm
L = π * 50 cm * acos((50 cm - 25 cm) / 50 cm) = π * 50 cm * acos(0.5) = 164.49 cm (approx.)

Answer 2

It is easy to calculate the sine of an angle from the figure, see: Trigonometric_functions
Find the angle by the sine.
Angle is the circumference of a circle.