An Airplane Crashes in a Lake and Is Spotted by Observers

Multiple Choice

An airplane crashes in a lake and is spotted by observers at lighthouses A and B along the coast. Lighthouse B is 1.10 miles due east of lighthouse A. The bearing of the airplane from lighthouse A is $\mathrm { S } 20 ^ { \circ } \mathrm { E }$ ; the bearing of the plane from lighthouse B is $\mathrm { S } 40 ^ { \circ } \mathrm { W }$ . Find the distance from each lighthouse to the crash site.

A) Distance from lighthouse $A$ : 0.95 miles, Distance from lighthouse $B$ : 1.28 miles
B) Distance from lighthouse $A$ : 1.35 miles, Distance from lighthouse $B$ : 0.97 miles
C) Distance from lighthouse $A$ : 0.92 miles, Distance from lighthouse $B$ : 0.76 miles
D) Distance from lighthouse $A$ : 1.43 miles, Distance from lighthouse $B$ : 0.84 miles
E) Distance from lighthouse $A$ : 0.97miles, Distance from lighthouse $B$ : 1.19 miles