Question is in the description

Question

Two patrol boats leave cape May at the same time,the same speed, but on different bearings l. One has bearing 40° 47' the other has bearing 52° 18'. How far apart will they be when they are 23 miles from cape may

Answer 1

Use the law of cosines.

 

40° 47' ≅ 40.78º

52º 18' = 52.3º

 

θ = (52.3 - 40.78)° = 11.52°

 

c = distance between them

 

c² = a² + b² - 2ab cosθ = 23² + 23² - 2(23)(23)cos11.52º ≅ 21.31

 

c = √21.31 miles ≅ 4.62 miles