Trigonometry - Law of sines, Bearing, Ship, Motorboat, Navy, Marines, Sailor

1. A ship takes a sighting of two motorboats. Motorboat A has a bearing of N 44 W and Motorboat B has a bearing of N 59 E. The distance between the two motorboats is 4 km and the bearing of Motorboat B from A is N 88 E. Compute the distance of the ship from each motorboat.
find:

SA = distance of the ship from Motorboat A

SB = distance of the ship from Motorboat B


given:

Bearing of Motorboat A = N 44 W

Bearing of Motorboat B = N 59 E

Bearing of Motorboat B from A = N 88 E

AB = 4 km, distance between Motorboat A and Motorboat B


solution:


A_B
S\/

angle ASB = 44 + 59 = 103

angle BAS = 180 - 88 - 44 = 48

angle ABS = 180 - 103 - 48 = 29


using Sine Law:

SA/sin ABS = SB/sin BAS = AB/sin ASB

SA/sin 29 = AB/sin 103

SA/0.485  = 4/0.974 

SA = 0.485 * 4/0.974

SA = 1.99 km


SB/sin 48 = AB/sin 103

SB/0.743 = 4/0.974

SB = 0.743 * 4/0.974

SB = 3.05 km