Solve the Problem $\mathrm { A }$ And $\mathrm { B } , 8.68 \mathrm { mi }$

Solve the problem.
-Radio direction finders are set up at points $\mathrm { A }$ and $\mathrm { B } , 8.68 \mathrm { mi }$ apart on an east-west line. From $\mathrm { A }$ it is found that the bearing of a signal from a transmitter is $\mathrm { N } 54.3 ^ { \circ } \mathrm { E }$ , while from $\mathrm { B }$ it is $\mathrm { N } 35.7 ^ { \circ } \mathrm { W }$ . Find the distance of the transmitter from $\mathrm { B }$ , to the nearest hundredth of a mile.

A) $4.57 \mathrm { mi }$
B) $5.07 \mathrm { mi }$
C) $7.05 \mathrm { mi }$
D) $7.55 \mathrm { mi }$