(a) The standard unit of angle is degrees and its subdivisions minutes and seconds. An alternate unit is radians, defined in Figure 1.13. Verify that $180^{\circ}=\pi$ radians. Notice that for small angles, the length of the arc ABP is approximately equal to the chord AP . Hence $\theta$ is approximately equal to $\mathrm{D} / \mathrm{r}$ for small angles.
(b) Another unit of angle is hours, the same as the unit of time. In this case, $360^{\circ}=24^{\mathrm{h}}$ or $1^{\mathrm{h}}=15^{\circ}$, where the superscript (h) denotes hours. Each hour is further subdivided into minutes and seconds in direct analogy with time units. For example, $50^{\circ}=3^{\mathrm{h}} 20^{\mathrm{m}}$, that is, 3 hours and 20 minutes. Convert $40^{\circ}$ and $160^{\circ}$ into time units (hours, minutes, and seconds).