Problem 80E

80. A right triangle $A B C$ is given with $\angle A=\theta$ and $|A C|=b$. $C D$ is drawn perpendicular to $A B, D E$ is drawn perpendicular to $B C, E F \perp A B$, and this process is continued indefinitely, as shown in the figure. Find the total length of all the perpendiculars

$$|C D|+|D E|+|E F|+|F G|+\cdots$$

in terms of $b$ and $\theta$.

Step-by-Step Solution