## Precalculus (6th Edition) Blitzer

The required solution is $2.5\ \text{radians}$ or $143.23{}^\circ$
The radius of the earth $r$ is $4000\ \text{miles}$. The distance $s$ between A and B is $10,000\ \text{miles}$. The angle $\theta$ at the center between A and B is given by $\theta =\frac{s}{r}$ Put $10,000\ \text{miles}$ for $s$ and $4000\ \text{miles}$ for $r$: \begin{align} & \theta =\frac{10,000\ \text{miles}}{4000\ \text{miles}} \\ & =2.5\ \text{radians} \end{align} Convert $\theta$ into degrees: \begin{align} & \theta =2.5\ \text{radians}\left( \frac{180{}^\circ }{\pi \ \text{radians}} \right) \\ & =\left( \frac{2.5}{\pi } \right)180{}^\circ \end{align} Put $\pi =3.14159$: \begin{align} & \theta =\left( \frac{2.5}{3.14159} \right)180{}^\circ \\ & =\left( 0.79577 \right)180{}^\circ \\ & =143.23{}^\circ \end{align}