Ζικ Ζακ

The diameter of a semicircular arc is $A_0{A}_1=1$. A point $A_2$ is selected on the arc, such that $\angle A_0{A}_1{A}_2=1^0$. Then a point $A_3$ is selected on the arc $A_1{A}_2$, such that $\angle A1A2A3=2^0$. 

The procedure is continued: point $A_{k+1}$ is selected on the arc $A_{k-1}{A}_k$, so that the measure of angle $A_{k-1}{A}_k{A}_{k+1}$ is $k$ degrees ($k=3,4,\dots ,9$). What will be the length of the line segment $A_9{A}_{10}$? (The figure is not to scale.)

KöMaL Problems in Mathematics, November 2021