Answer
(a) $89.054^\circ$
(b) $235,894mi$
Work Step by Step
(a) Use the figure given in the problem, since angle $\theta$ corresponds to an arc length of $6155mi$ and we know the radius of the Earth as $3960mi$, we have $\theta=\frac{6155}{3960}\approx1.5543rad\approx89.054^\circ$
(b) We label the center of the Earth with letter $E$ and label the point on the Moon with letter $M$. in the right triangle of $\Delta MEB$, $cos\theta=\frac{EB}{ME}$ so that $ME=\frac{EB}{cos\theta}=\frac{3960}{cos89.054^\circ}\approx239854mi$ and the distance from point A to the moon is $AM=ME-EA=239854-3960=235,894mi$
