Chapter 5.1, Problem 72E

Comparing a Triangle and a Sector of a Circle Two wood sticks and a metal rod, each of length, are connected to form a triangle with angle ${\theta }_1$ at the point $P$, as shown in the first figure below. The rod is then bent to form an arc of a circle with center $P,$ resulting in a smaller angle ${\theta }_2$ at the point $P,$ as shown in the second figure. Find ${\theta }_1$, ${\theta }_2$ and ${\theta }_1-{\theta }_2$