Solve the Problem $2.7$ Miles Apart $24 ^ { \circ }$ And Telescope B Reports an Angle of Elevation Of

Multiple Choice

Solve the problem.
-A rocket tracking station has two telescopes A and B placed $2.7$ miles apart. The telescopes lock onto a rocket and transmit their angles of elevation to a computer after a rocket launch. What is the distance to the rocket from telescope B at the moment when both tracking stations are directly east of the rocket telescope A reports an angle of elevation of $24 ^ { \circ }$ and telescope B reports an angle of elevation of $51 ^ { \circ }$ ? Round to the nearest hundredth of a mile.

A) $5.16 \mathrm { mi }$
B) $2.42 \mathrm { mi }$
C) $1.41 \mathrm { mi }$
D) $4.62 \mathrm { mi }$