An airplane crashes in a lake and is spotted by observers at

An airplane crashes in a lake and is spotted by observers at lighthouses A and B along the coast. Lighthouse B is 1.50 miles due east of lighthouse A. The bearing of the airplane from lighthouse A is S20 degree E: the bearing of the plane from lighthouse B is S42 degree W. Find the distance from each lighthouse to the crash site. (Round your final answer to two decimal places.)

Solution

Solution:

Here;

Let C be the position of the crashsite.

=><ABC=90*-42*=48*

=> AC/sin48*=1.5/sin(20*+48*)

=> AC=1.5sin48* / sin68*

=> AC = 1.20226 miles

or 1.20 miles