<PRE><B>Question 935601</B>
Two ships leave the docks D, at the same time Princess Pearl P, sails on a bearing of 160 degrees at a speed of 18 km/hour and a Regal rose R, sales on a bearing of 105 degrees.
 After two hours the angle DRP is 80 degree.
:
Draw at triangle DPR, 
side DP: 2*18 = 36 km
Angle D: 160-105 = 55 degrees
Angle R: Given as 80 degrees
Angle P: 180-55-80 = 45 degrees
Find
a-The distance between the ships at this time
Let d = distance between the ship R to P
Use the law of sines
{{{d/sin(55)}}} = {{{36/sin(80)}}}
find the sines and cross multiply
.985d = .819*36
d = 29.49/.985
d = 29.9 km apart
:
b- The speed of the Regal Rose
let p = the distance traveled by the Regal Rose
{{{p/sin(45)}}} = {{{36/sin(80)}}}
.985p = .707*36
p = 25.452 km
Find the speed
25.452/2 = 12.7 km/hr</PRE>